Two convex lenses of focal lengths 20 cm and 30 cm are placed in contact with each other co-axially. The focal length of the combination is:
1
60 cm
2
10 cm
3
12 cm
4
40 cm
Official Solution
Correct Option: (3)
To solve the problem, we need to find the effective focal length of two convex lenses placed in contact.
1. Formula for Combination of Lenses in Contact:
When two lenses are in contact, their combined focal length is given by:
Where:
- = focal length of first lens = 20 cm
- = focal length of second lens = 30 cm
2. Substitute the Values:
Take LCM:
3. Solve for :
cm
Final Answer:
The focal length of the combination is 12 cm.
02
PYQ 2023
medium
physicsID: ts-eamce
A source and an observer move away from each other with same velocity of 10 m-1 with respect to the ground. If the observer finds the frequency of sound coming from the source as 1980 Hz, then the actual frequency of the source is (speed of sound in air = 340 ms-1)
1
1950 Hz
2
2100 Hz
3
2132 Hz
4
2486 Hz
Official Solution
Correct Option: (2)
To solve the problem, we need to find the actual frequency of the source using the Doppler effect when both the source and observer are moving away from each other with the same velocity.
1. Doppler Effect Formula (for sound):
The observed frequency when both the source and observer are moving is given by:
Where:
- = observed frequency (1980 Hz)
- = actual frequency (to be found)
- = speed of sound in air (340 m/s)
- = velocity of the observer (10 m/s, moving away → use positive)
- = velocity of the source (10 m/s, moving away → use positive)
2. Plug in the Known Values:
3. Solve for :
Final Answer:
The actual frequency of the source is 2100 Hz.
03
PYQ 2024
hard
physicsID: ts-eamce
When an object of height 12 cm is placed at a distance from a convex lens, an image of height 18 cm is formed on a screen. Without changing the positions of the object and the screen, if the lens is moved towards the screen, another clear image is formed on the screen. The height of this image is.
1
2
3
4
\bigskip
Official Solution
Correct Option: (3)
Step 1: In this problem, we can use the magnification formula for lenses: Given that the object height is 12 cm and the first image height is 18 cm, the magnification is: This magnification is the same for the second image when the lens is moved, and the object height remains the same. Therefore, the second image will have a magnification of 1.5 times the object height. The second image height will be: However, the magnification changes when the lens is moved, and the image height is reduced to 8 cm. Thus, the second image height is . \bigskip
04
PYQ 2024
medium
physicsID: ts-eamce
A boy of height 1.2 m is standing in front of a large concave mirror of radius of curvature 20 m at a distance of 40 m from the mirror. The distance of the image of the boy from the boy is:
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: The mirror formula for concave mirrors is given by:
where:
- is the focal length of the mirror,
- is the image distance,
- is the object distance (negative for real objects in front of the mirror).
Step 2: The focal length of the concave mirror is related to its radius of curvature by the equation:
Given that the radius of curvature , we get:
Step 3: The object distance (since the object is placed in front of the mirror). Now, substitute these values into the mirror formula:
Step 4: The distance of the image from the boy is the sum of the image distance and the object distance :
Step 5: The image of the boy is at a distance of from the boy. Thus, the correct answer is Option (2).
05
PYQ 2024
medium
physicsID: ts-eamce
Two positive point charges of and are kept in air with a separation of 12 cm.- To make the distance between the charges 4 cm, the work done is
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Work Done in Moving Charges The work done in moving two point charges from an initial separation to a final separation is given by the formula: where: - (Coulomb’s constant), - , - , - , - .
Step 2: Substituting Values Thus, the correct answer is .
06
PYQ 2024
easy
physicsID: ts-eamce
A small-angled prism is made of a material of refractive index . The ratio of the angles of minimum deviations when the prism is placed in air and in water of refractive index is:
Official Solution
Correct Option: (1)
07
PYQ 2024
hard
physicsID: ts-eamce
A convex lens of focal length 20 cm is immersed in a liquid of refractive index 1.3. If the refractive index of the material of the lens is 1.5, then the focal length of the lens when immersed in the liquid is:
1
cm
2
cm
3
cm
4
cm
Official Solution
Correct Option: (3)
Step 1: Lens Maker's Formula in a Medium The focal length of a lens in a medium is given by the modified lens maker’s formula: where: - is the focal length in the medium, - is the refractive index of the lens, - is the refractive index of the medium, - cm is the original focal length in air.
Step 2: Substituting Given Values
Step 3: Solving for
Step 4: Verifying the Correct Option Comparing with the given options, the correct answer is:
08
PYQ 2024
medium
physicsID: ts-eamce
In Young's double slit experiment, the wavelength of the monochromatic light used is , the distance between the slits is and the distance of the screen from the plane of the slits is 100 cm. If the maximum intensity on the screen is , then the intensity at a point on the screen which is at 5 cm from the central maximum is:
1
2
3
4
Official Solution
Correct Option: (1)
We know that the intensity at a point in Young’s double slit experiment is given by:
Where is the distance between the slits, is the wavelength, and is the angle of diffraction. The angle for a distance from the central maximum is given by:
Substitute the values for and the given value for :
Since , the intensity is:
09
PYQ 2024
medium
physicsID: ts-eamce
An object placed at a distance of 24 cm from a concave mirror forms an image at a distance of 12 cm from the mirror. If the object is moved with a speed of 12 ms , then the speed of the image is:} \vspace{0.5cm}
1
24 ms
2
3 ms
3
6 ms
4
12 ms
Official Solution
Correct Option: (2)
Step 1: Use the Mirror Formula The mirror formula is: where: - cm (object distance), - cm (image distance).
Step 2: Find the Magnification Magnification is given by:
Step 3: Find Image Velocity Since the velocity of the object is ms , the velocity of the image is: Thus, the correct answer is:
10
PYQ 2024
easy
physicsID: ts-eamce
When the object and the screen are 90 cm apart, it is observed that a clear image is formed on the screen when a convex lens is placed at two positions separated by 30 cm between the object and the screen. The focal length of the lens is:
1
21.4 cm
2
20 cm
3
30 cm
4
30.8 cm
Official Solution
Correct Option: (2)
Step 1: Use the Lens Formula The given data states that the object and screen are 90 cm apart, and the convex lens can be placed at two positions separated by 30 cm. Let cm be the distance between the object and the screen, and let cm be the separation between the two lens positions.
Step 2: Use the Lens Formula for Two Positions The focal length of the convex lens is given by: Substituting the given values: Thus, the correct answer is:
11
PYQ 2024
medium
physicsID: ts-eamce
The refractive index of the material of a small angled prism is . If the angle of minimum deviation is , the angle of the prism is?
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Use the prism formula For a small-angled prism, the refractive index ( ) is related to the angle of the prism ( ) and the angle of minimum deviation ( ) by the formula: Given: For small angles (in degrees), we approximate: Step 2: Solve for Rewriting the equation: Multiplying by 2: Thus, the angle of the prism is .
12
PYQ 2024
medium
physicsID: ts-eamce
The diameter of the objective of a telescope is 3.6 m. The limit of resolution of the telescope for a light of wavelength 540 nm is:
1
rad
2
rad
3
rad
4
rad
Official Solution
Correct Option: (2)
Step 1: Understanding the Rayleigh Criterion. The limit of resolution (θ) of a telescope is given by Rayleigh's criterion: where: - is the wavelength of light (540 nm = m), - is the diameter of the telescope’s objective (3.6 m), - The factor is derived from diffraction theory.
Step 2: Substituting the values.Final Answer:
13
PYQ 2024
hard
physicsID: ts-eamce
A thin plano-convex lens of focal length 73.5 cm has a circular aperture of diameter 8.4 cm. If the refractive index of the material of the lens is , then the thickness of the lens is nearly.
1
2
3
4
\bigskip
Official Solution
Correct Option: (3)
Step 1: For a plano-convex lens, the approximate thickness of the lens can be calculated using the formula: where is the radius of curvature, and is the refractive index. Here, , and . Now, substituting the values: The thickness of the lens is approximately .
14
PYQ 2024
medium
physicsID: ts-eamce
As shown in the figure, a block is placed in front of a convex lens. Choose the most appropriate image of the block from the following options:
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: The image formation by a convex lens depends on the object's position relative to the focal point and the lens. - If the object is placed between the focus and the lens, the image formed will be virtual, upright, and magnified. - If the object is placed beyond twice the focal length, the image formed will be real, inverted, and diminished.
Step 2: In this case, the block is placed in front of the convex lens at a distance beyond (twice the focal length), so the image formed will be real, inverted, and diminished.
Step 3: According to the given options, the image that fits the description of a real, inverted, and diminished image is Option 2.
15
PYQ 2024
medium
physicsID: ts-eamce
A boy of height 1.2 m is standing in front of a large concave mirror of radius of curvature 20 m at a distance of 40 m from the mirror. The distance of the image of the boy from the boy is:
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: The mirror formula for concave mirrors is given by:
where:
- is the focal length of the mirror,
- is the image distance,
- is the object distance (negative for real objects in front of the mirror). Step 2: The focal length of the concave mirror is related to its radius of curvature by the equation:
Given that the radius of curvature , we get:
Step 3: The object distance (since the object is placed in front of the mirror). Now, substitute these values into the mirror formula:
Step 4: The distance of the image from the boy is the sum of the image distance and the object distance :
Step 5: The image of the boy is at a distance of from the boy. Thus, the correct answer is Option (2).
16
PYQ 2024
medium
physicsID: ts-eamce
The Brewster angle for air to glass transition of light is (Refractive index of glass =
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding Brewster's Law Brewster's angle is the angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface without any reflection. It is given by: where is the refractive index of the second medium (glass) concerning the first medium (air).
Step 2: Apply the given values Given , the Brewster angle is:
Step 3: Identify the correct option From the given answer choices, the correct expression is: Thus, the correct answer is Option (3).
17
PYQ 2024
medium
physicsID: ts-eamce
For a combination of two convex lenses of focal lengths and to act as a glass slab, the distance of separation between them is:
1
2
3
4
Official Solution
Correct Option: (1)
For two convex lenses to act as a glass slab, the net optical path difference should be zero. This happens when the separation between the lenses is equal to the sum of their focal lengths:
18
PYQ 2024
medium
physicsID: ts-eamce
When a light ray incident on an equilateral prism, the angle of minimum deviation is found to be half of the angle of prism. The refractive index of the material of the prism is:
1
1.5
2
2
3
4
Official Solution
Correct Option: (4)
Let the angle of prism be and the angle of minimum deviation be . Given: For a prism, the refractive index is given by the formula: Substitute into the formula: For an equilateral prism, the angle of prism . Thus:
Thus, the refractive index of the material of the prism is .
19
PYQ 2024
medium
physicsID: ts-eamce
A charged particle of mass 5 g and charge 20 μC is thrown with a velocity of 16 m/s in a direction opposite to the direction of a uniform electric field of N/C. The distance travelled by the particle before coming to rest is:
1
2
3
4
Official Solution
Correct Option: (3)
Step 1: Identifying the Forces Acting on the Particle - The charged particle experiences a force due to the electric field: Step 2: Calculating Acceleration using Newton’s Second Law - Using , the acceleration is: Step 3: Applying Kinematic Equation - Using the equation (since motion is opposite to acceleration):
20
PYQ 2024
easy
physicsID: ts-eamce
If you are using eyeglasses of power , your near point is:
1
cm
2
cm
3
cm
4
cm
Official Solution
Correct Option: (2)
The power of a lens is given by: where: - is the power in diopters (D), - is the focal length in centimeters. For : The near point of a person using glasses is the focal length of the corrective lens. Thus, the correct answer is .
21
PYQ 2024
easy
physicsID: ts-eamce
A block is placed in front of a convex lens as shown in the figure. Choose the most appropriate image of the block from the following options:
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: The image formation by a convex lens depends on the position of the object relative to the focal point and the lens. - If the object is placed between the focus and the lens, the image formed will be virtual, upright, and magnified.
- If the object is placed beyond twice the focal length, the image formed will be real, inverted, and diminished. Step 2: In this case, the block is placed in front of the convex lens at a distance beyond (twice the focal length), so the image formed will be real, inverted, and diminished. Step 3: According to the given options, the image that fits the description of a real, inverted, and diminished image is Option 2.
22
PYQ 2024
medium
physicsID: ts-eamce
The power of a thin convex lens placed in air is . The refractive index of the material of the convex lens is . If this convex lens is immersed in a liquid of refractive index , then:
1
It behaves like a convex lens of focal length 75 cm
2
It behaves like a convex lens of focal length 125 cm
3
It behaves like a concave lens of focal length 125 cm
4
It behaves like a concave lens of focal length 75 cm
Official Solution
Correct Option: (3)
Step 1: Using Lens Maker's Formula The power of a lens in air is given by the lens maker's formula: where , (refractive index of lens), and (refractive index of air). The focal length in air is:
Step 2: Finding Power in the Liquid Medium When the lens is placed in a medium of refractive index , the power is given by: Substituting the values: Simplifying: Since the power is negative, the lens behaves as a concave lens. The focal length is:
Step 3: Conclusion Thus, the lens behaves like a concave lens with a focal length of 125 cm:
23
PYQ 2024
medium
physicsID: ts-eamce
If a ray of light passes through an equilateral prism such that the angle of incidence and the angle of emergence are both equal to 70\% of the angle of the prism, then the angle of minimum deviation is:
1
2
3
4
Official Solution
Correct Option: (4)
For an equilateral prism with angle , when the angle of incidence and emergence are equal, the condition for minimum deviation holds: Given : For an equilateral prism, :
24
PYQ 2025
easy
physicsID: ts-eamce
A ray of light is travelling from a medium of refractive index 1.414 to air. If the angle of incidence is , then the angle of deviation of the light ray is
Official Solution
Correct Option: (1)
25
PYQ 2025
easy
physicsID: ts-eamce
A convex lens made of glass of refractive index 1.5 is immersed in a liquid. If the focal length of the lens when immersed in the liquid is twice its focal length when it is in air, then the refractive index of the liquid is
Official Solution
Correct Option: (1)
26
PYQ 2025
medium
physicsID: ts-eamce
A ray of light incidents at an angle of on one face of a small angle prism of refracting angle . If the ray of light emerges normally from the second face, the refractive index of the material of the prism is
1
1.40
2
1.45
3
1.55
4
1.50
Official Solution
Correct Option: (3)
Step 1: State the relations for a small-angle prism.
For a small-angle prism, the angles of incidence ( ), refraction ( ), emergence ( ), and the refracting angle ( ) are related by:
1.
2. Snell's Law at the first face: . For small angles, .
3. Snell's Law at the second face: . For normal emergence, .
Step 2: Apply the condition for normal emergence.
If the ray emerges normally from the second face, the angle of emergence is , and the angle of refraction at the second face, , is also .
.
Step 3: Find the angle of refraction at the first face.
Using the prism relation :
.
We are given the refracting angle . So, .
Step 4: Use Snell's Law at the first face to find the refractive index .
Snell's Law at the first face (incidence ) is .
We are given and we found .
Step 5: Calculate the numerical value.
We use the small angle approximation (in radians) for the ratio of the angles:
(The approximation is accurate for this ratio).
The refractive index is .
27
PYQ 2025
medium
physicsID: ts-eamce
A straight metal rod of length 6 cm is placed along the principal axis of a concave mirror of focal length 9 cm such that the end of the rod closer to the mirror is at a distance of 15 cm from the pole of the mirror. The length of the image of the rod is
1
6 cm
2
12 cm
3
8.75 cm
4
6.75 cm
Official Solution
Correct Option: (4)
Step 1: Define the sign convention and given values.
The mirror is concave, so the focal length is negative. cm.
The rod lies along the principal axis. The end closer to the mirror is .
The distance of end from the pole is cm (since the object is in front of the mirror).
The length of the rod is cm.
The distance of the far end, , is cm.
Step 2: Calculate the image distance for the nearer end A.
We use the mirror formula: .
Step 3: Calculate the image distance for the farther end B.
We use the mirror formula again for cm.
Step 4: Calculate the length of the image.
Since the object is placed beyond the focal point, the image formed is real and inverted, and lies between the focus and the center of curvature.
The length of the image, , is the absolute difference between the image distances of the two ends.
28
PYQ 2025
medium
physicsID: ts-eamce
A convex lens of radii of curvature 6 cm and 12 cm is immersed in a liquid of refractive index 1.3. If the refractive index of the material of the lens is 1.5, then the focal length of the lens when immersed in the liquid is
1
39 cm
2
13 cm
3
26 cm
4
52 cm
Official Solution
Correct Option: (3)
We use the Lens Maker's formula for a lens in a medium. . We are given: Refractive index of the lens material, . Refractive index of the liquid medium, . Radii of curvature for a convex lens: one is positive, the other is negative. Let cm and cm. Now, substitute the values into the formula: . . . . . Therefore, the focal length of the lens in the liquid is cm.
29
PYQ 2025
medium
physicsID: ts-eamce
A Cassegrain telescope uses two mirrors of radii of curvature 25 cm and 16 cm separated by a distance of 2.5 cm. The position of the final image of an object at infinity is
1
40 cm from convex mirror
2
4.44 cm from concave mirror
3
4.44 cm from convex mirror
4
40 cm from concave mirror
Official Solution
Correct Option: (1)
In a Cassegrain telescope, the primary mirror is a concave mirror and the secondary mirror is a convex mirror. Object is at infinity, so the primary (concave) mirror forms an image at its focus. For the primary mirror: Radius of curvature cm (concave). Focal length cm. The image is formed at the focus, 12.5 cm from the primary mirror. This image acts as a virtual object for the secondary (convex) mirror. The distance between the mirrors is cm. The object distance for the secondary mirror ( ) is the distance from the secondary mirror to .
The secondary mirror is between the primary mirror and its focus.
cm. (The object is virtual, so is positive). For the secondary mirror: Radius of curvature cm (convex). Focal length cm. Now, we use the mirror formula for the secondary mirror to find the final image position ( ). . . . cm. Since is positive, the final image is formed 40 cm to the right of the secondary (convex) mirror.
30
PYQ 2025
medium
physicsID: ts-eamce
Monochromatic light of wavelength 6000 Å incidents on a small angled prism. If the angle of the prism is 6°, the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48, then the angle of dispersion produced for this incident light is
1
30°
2
36°
3
0.24°
4
0°
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept:
Angular dispersion is the difference in the angles of deviation for two different wavelengths (colors) of light after passing through a dispersive medium like a prism. For a prism with a small angle, the deviation itself is small, and a simplified formula can be used. Step 2: Key Formula or Approach:
For a small-angled prism, the angle of deviation is given by:
where is the angle of the prism and is the refractive index of the material.
The angular dispersion between violet and red light is the difference in their deviations:
The wavelength of the incident light (6000 Å) is not needed to calculate the angular dispersion between violet and red, as their refractive indices are already given. Step 3: Detailed Explanation:
We are given the following values:
- Angle of the prism, .
- Refractive index for violet light, .
- Refractive index for red light, .
Using the formula for angular dispersion: Step 4: Final Answer:
The angle of dispersion is . The given options are numerically incorrect, likely due to a typographical error in the question paper. Option (C), which is listed as 24°, is probably meant to be 0.24°. Based on the calculation, the correct value is 0.24°.
31
PYQ 2025
medium
physicsID: ts-eamce
An object of height 3.6 cm is placed normally on the principal axis of a concave mirror of radius of curvature 30 cm. If the object is at a distance of 10 cm from the principal focus of the mirror, then the height of the real image formed due to the mirror is
1
5.4 cm
2
3.6 cm
3
1.8 cm
4
2.7 cm
Official Solution
Correct Option: (1)
Step 1: Understanding the Concept:
This problem requires the use of the mirror formula to find the image position and the magnification formula to find the image height. It's crucial to use the correct sign convention for all quantities. For a concave mirror, the focal length and radius of curvature are negative. Distances measured in the direction of incident light are positive, and those opposite are negative. Step 2: Key Formula or Approach:
- Mirror Formula:
- Magnification:
where is focal length, is image distance, is object distance, is image height, and is object height. Step 3: Detailed Explanation: Determine the parameters from the question:
- Object height, cm (placed normally, so considered upright).
- Radius of curvature, cm (concave mirror).
- Focal length, cm.
- The object is "10 cm from the principal focus". The focus is at x = -15 cm. For a real image to be formed by a concave mirror, the object must be placed beyond the focus. Therefore, the object position is farther from the mirror than the focus.
- Object distance, cm. Calculate the image distance (v):
Using the mirror formula:
The negative sign indicates that the image is formed on the same side as the object and is therefore a real image, which is consistent with the question. Calculate the image height ( ):
Using the magnification formula:
The negative sign indicates the image is inverted. The height (magnitude) of the image is 5.4 cm. Step 4: Final Answer:
The height of the real image is 5.4 cm. Therefore, option (A) is correct.
32
PYQ 2025
medium
physicsID: ts-eamce
A convex lens produces clear images when placed at two positions between an object and a screen that are 1 m apart. If the distance between the two positions of the lens at which clear images are formed is 20 cm, the focal length of the lens is:
1
5 cm
2
24 cm
3
125 cm
4
12 cm
Official Solution
Correct Option: (4)
• Let the object-screen distance and separation between lens positions . • For lens displacement method: . Wait, the formula is correct: , so correct answer is (2) 24 cm. • Hence, focal length = 24 cm.
33
PYQ 2025
medium
physicsID: ts-eamce
A layer of oil of thickness 5.8 cm is floating on a water layer of thickness 8 cm. If the total apparent depth is 10 cm and the refractive index of water is 3/4, then the refractive index of oil is
The distance between the objective and eyepiece of an astronomical telescope when the final image forms at infinity is 62 cm. If the magnification of the telescope is 30, the focal lengths of the objective and eyepiece respectively are:
1
31 cm, 2 cm
2
2 cm, 31 cm
3
2 cm, 60 cm
4
60 cm, 2 cm
Official Solution
Correct Option: (1)
• For astronomical telescope: , magnification . • Let , . Wait, distance between lenses = , so yes , which matches option (1). • Hence, focal lengths are 60 cm and 2 cm.
35
PYQ 2025
medium
physicsID: ts-eamce
In the experiment of a convex lens, if the distance between the object and its real image is 90 cm and the magnification produced by the lens is 2, then the focal length of the convex lens is
