The diameter of the objective of a telescope is a, its magnifying power is m and wavelength of light is λ. The resolving power of the telescope is
1
(1.22λ)/a
2
(1.22a)/λ
3
λ m/(1.22a)
4
a/(1.22λ)
Official Solution
Correct Option: (4)
Step 1: Angular resolution:
θ=(1.22λ)/(a) Step 2: Resolving power =(1)/(θ)=(a)/(1.22λ).
02
PYQ 2011
medium
physicsID: bitsat-2
A thin convergent glass lens (= 1.5) has a power of +5.0 D. When this lens is immersed in a liquid of refractive index μ, it acts as a divergent lens of focal length 100 cm. The value of μ must be:
1
(4)/(3)
2
(5)/(3)
3
(5)/(4)
4
(6)/(5)
Official Solution
Correct Option: (2)
Step 1: Power of lens in air.
P = ( - 1)((1)/(R₁) - (1)/(R₂)) = 5 Step 2: Power of lens in liquid.
P' = (()/(μ) - 1)((1)/(R₁) - (1)/(R₂)) Step 3: Given focal length in liquid.
P' = -1 D Step 4: Solving ratio.
(P')/(P) = ()/(μ) - 1 - 1 μ = (5)/(3)
03
PYQ 2011
medium
physicsID: bitsat-2
A vessel of depth d is half-filled with a liquid of refractive index ₁ and the upper half with a liquid of refractive index ₂. The apparent depth of the vessel seen perpendicularly is:
1
d(₁₂)/(₁+₂)
2
d((1)/(₁)+(1)/(₂))
3
2d((1)/(₁)+(1)/(₂))
4
2d((1)/(₁₂))
Official Solution
Correct Option: (2)
Step 1: Apparent depth formula.
Apparent depth = real depthμ Step 2: Applying to two layers.
dₐ = (d/2)/(₁) + (d/2)/(₂) Step 3: Simplifying.
dₐ = d((1)/(₁)+(1)/(₂))
04
PYQ 2012
medium
physicsID: bitsat-2
A ray of light is incident at the glass-water interface at an angle , it emerges finally parallel to the surface of water, then the value of would be:
1
2
3
4
1
Official Solution
Correct Option: (2)
Step 1: Refraction at the interface.
When light emerges from the water surface parallel to the surface, the angle of incidence must satisfy the critical angle condition, where the refracted angle is . Using Snell's law:
Thus, the correct answer is (2).
05
PYQ 2013
medium
physicsID: bitsat-2
When light is refracted, which of the following does not change?
1
Wavelength
2
Frequency
3
Velocity
4
Amplitude
Official Solution
Correct Option: (2)
Step 1: Understand the concept of refraction. In refraction, the light changes its direction as it passes from one medium to another, which causes its velocity and wavelength to change. However, the frequency remains unchanged since it depends only on the source. Step 2: Conclusion. The frequency of light does not change during refraction.
Final Answer:
06
PYQ 2015
medium
physicsID: bitsat-2
A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials of refractive indices and and is the radius of curvature of the curved surfaces of the lenses, then the focal length of the combination is:
1
2
3
4
Official Solution
Correct Option: (1)
Step 1: Power of plano-convex lens:
Step 2: Power of plano-concave lens:
Step 3: Net power:
Step 4: Focal length:
07
PYQ 2016
medium
physicsID: bitsat-2
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:
A biconvex lens has a radius of curvature of magnitude 20cm. Which of the following options best describe the image formed of an object of height 2cm placed 30cm from the lens?
Two plano-concave lenses (1 and 2) of glass of refractive index 1.5 have radii of curvature 25 cm and 20 cm. They are placed in contact with their curved surfaces towards each other and the space between them is filled with liquid of refractive index 4/3. The combination is
1
convex lens of focal length 70 cm
2
concave lens of focal length 70 cm
3
concave lens of focal length 66.6 cm
4
convex lens of focal length 66.6 cm
Official Solution
Correct Option: (3)
Step 1: Power of each curved surface using refraction formula Net power:
P = ((mul)/(mug)-1)((1)/(R₁)-(1)/(R₂)) Step 2: Substituting values gives
P = -(1)/(66.6)cm⁻1
10
PYQ 2017
medium
physicsID: bitsat-2
On a hypotenuse of a right angled prism of liquid is placed as shown in the figure. Light is allowed to fall normally on the short face of the prism. In order that the ray of light may be totally reflected, the maximum value of refractive index is
1
1.30
2
1.47
3
1.20
4
1.25
Official Solution
Correct Option: (2)
Step 1: For total internal reflection,
sin c = (1)/(μ) Step 2: From prism geometry, the angle of incidence at the hypotenuse is fixed. Step 3: Maximum μ corresponds to the critical condition.
11
PYQ 2017
medium
physicsID: bitsat-2
On a hypotenuse of a right prism of refractive index , a drop of liquid is placed as shown in figure. Light is allowed to fall normally on the short face of the prism. In order that the ray of light may get totally reflected, the maximum value of refractive index is :
1
1.3
2
1.47
3
1.2
4
1.25
Official Solution
Correct Option: (1)
for total internal infliction By snells low
12
PYQ 2018
medium
physicsID: bitsat-2
A point object O is placed in front of a glass rod having spherical end of radius of curvature 30cm. The refractive index of glass is μ = 1.5. The image would be formed at:
1
30 cm left
2
infinity
3
1 cm to the right
4
18 cm to the left
Official Solution
Correct Option: (2)
Step 1:
Refraction at a spherical surface:
(mu₂)/(v) - (mu₁)/(u) = (mu₂ - mu₁)/(R) Step 2:
Substitute values:
mu₁ = 1, mu₂ = 1.5, u = -15cm, R = 30cm Step 3:
(1.5)/(v) + (1)/(15) = (0.5)/(30)
⟹ (1.5)/(v) = 0 Step 4:
v = ∞
13
PYQ 2019
medium
physicsID: bitsat-2
A planoconvex lens fits exactly into a planoconcave lens. Their planar surfaces are parallel to each other. If the lenses are made of different materials of refractive indices mu₁ and mu₂ and R is the radius of curvature of the curved surface, then focal length of the combination is
1
2
3
4
(R)/(2-(mu₁+mu₂))
Official Solution
Correct Option: (1)
Step 1: Power of plano lenses:
P = (μ - 1)/(R) Step 2: Net power:
P = (mu₁ - 1)/(R) - (mu₂ - 1)/(R)
= (mu₁ - mu₂)/(R) Step 3: Focal length:
f = (1)/(P) = (R)/(mu₁ - mu₂)
14
PYQ 2020
medium
physicsID: bitsat-2
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:
1
lies between √(2) and 1
2
lies between 2 and √(2)
3
is less than 1
4
is greater than 2
Official Solution
Correct Option: (2)
Step 1: Prism formula at minimum deviation: Step 2: Given : Step 3: Since , lies between and Step 4:
15
PYQ 2020
medium
physicsID: bitsat-2
A bi-convex lens has a radius of curvature of magnitude 20cm. Which one of the following options best describes the image formed of an object of height 2cm placed 30cm from the lens?
1
Virtual, upright, height = 1cm
2
Virtual, upright, height = 0.5cm
3
Real, inverted, height = 4cm
4
Real, inverted, height = 1cm
Official Solution
Correct Option: (4)
Step 1: For a bi-convex lens (glass, μ=1.5):
(1)/(f) = (μ-1)((1)/(R₁)-(1)/(R₂))
(1)/(f) = 0.5((1)/(20)-(-1)/(20))=(1)/(20)
⟹ f=20cm Step 2: Lens formula:
(1)/(f) = (1)/(v) + (1)/(u)
(1)/(20) = (1)/(v) - (1)/(30)
⟹ v = 60cm Step 3: Magnification:
m = (v)/(u) = (60)/(30) = 2 Step 4: Image height:
hᵢ = m hₒ = 2 × 2 = 4cm
Image is real and inverted, hence effective height is 1cm.
16
PYQ 2021
medium
physicsID: bitsat-2
A telescope has an objective lens of 10cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000AA, is of the order of
1
6mm
2
6cm
3
6μm
4
6m
Official Solution
Correct Option: (1)
Step 1: By Rayleigh criterion, angular resolution: θ = (1.22λ)/(D)
Step 2: Linear separation: s = Lθ = (1.22λ L)/(D)
Step 3: Substituting values: λ = 5000AA = 5×10⁻7m, L = 1000m, D = 0.1m s = frac1.22 × 5×10⁻7 × 10000.1 ≈ 6×10⁻3m s ≈ 6mm
17
PYQ 2021
medium
physicsID: bitsat-2
On a hypotenuse of a right prism (30^∘-60^∘-90^∘) of refractive index 1.50, a drop of liquid is placed as shown in figure. Light is allowed to fall normally on the short face of the prism. In order that the ray of light may get totally reflected, the maximum value of refractive index of the liquid is
1
1.30
2
1.47
3
1.20
4
1.25
Official Solution
Correct Option: (2)
Step 1: Light enters the prism normally, so it travels undeviated inside.
Step 2: Angle of incidence at the hypotenuse: i = 60^∘
Step 3: For total internal reflection at prism–liquid interface: sin c = fracnlᵢqᵤᵢdnprism and i ≥ c
Step 4: Maximum nlᵢqᵤᵢd occurs when i=c: nlᵢqᵤᵢd = nprism sin i = 1.5 × sin 60^∘ nlᵢqᵤᵢd = 1.5 × frac√(3)2 ≈ 1.47
18
PYQ 2025
hard
physicsID: bitsat-2
A convex lens has focal length 20 cm. An object is placed at a distance of 40 cm from the lens. What is the position of the image formed?
1
40 cm on the opposite side
2
20 cm on the same side
3
20 cm on the opposite side
4
40 cm on the same side
Official Solution
Correct Option: (4)
The lens formula is given by: where: - (focal length of the lens) - (object distance; negative because the object is on the same side as the incoming light) We need to find the image distance . Rearranging the lens formula: Substituting the values: Thus, Since is positive, the image is formed on the opposite side of the object. The position of the image is 40 cm on the opposite side.
19
PYQ 2025
medium
physicsID: bitsat-2
Find the focal length of a lens in a compound lens system.
1
2
3
4
Official Solution
Correct Option: (1)
To solve the problem, we need to find the focal length of a lens in a compound lens system.
1. Understanding the Concept:
- Focal Length (f): The distance between the center of the lens and the point where parallel rays of light converge or diverge. - In a compound lens system, the total focal length of the system is related to the focal lengths of the individual lenses and by the formula:
2. Given Values:
- The focal lengths of the individual lenses, and .
3. Calculating the Total Focal Length:
The formula for the total focal length of a compound lens system is:
4. Final Answer:
The correct formula for the focal length in a compound lens system is , which corresponds to Option A.
20
PYQ 2025
medium
physicsID: bitsat-2
A concave mirror produces an image that is real, inverted, and diminished. What is the position of the object in relation to the mirror?
1
At the focal point
2
Between the focus and the mirror
3
Beyond twice the focal length
4
Between the focus and twice the focal length
Official Solution
Correct Option: (3)
For a concave mirror, the image formed is real, inverted, and diminished when the object is placed beyond twice the focal length ( ). The mirror equation is: where is the focal length, is the image distance, and is the object distance. If the object is beyond , the image formed is real, inverted, and diminished. Thus, the correct answer is:
21
PYQ 2025
easy
physicsID: bitsat-2
A radio wave travels in a medium with refractive index 1.5. What is the speed of light in this medium if the speed of light in vacuum is ?
1
2
3
4
Official Solution
Correct Option: (1)
The speed of light in a medium is related to the speed of light in vacuum and the refractive index by the formula: where: - (speed of light in vacuum), - (refractive index of the medium), - is the speed of light in the medium. Substituting the values: Thus, the speed of light in the medium is:
22
PYQ 2026
medium
physicsID: bitsat-2
A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R of identical shape and of same material as that of P are now combined as shown in the figure. The ray will now suffer
1
greater deviation
2
no deviation
3
same deviation as before
4
total internal reflection
Official Solution
Correct Option: (3)
Step 1: Understanding the Concept
Prism combinations can either add to the total deviation or cancel it out. When two identical prisms are placed in an opposite orientation (one upright, one inverted), they act like a parallel-sided glass slab. Step 2: Detailed Explanation
1. Prisms Q and R together form an inverted prism structure that is identical in shape to prism P.
2. When prism Q and R are combined with P in the configuration shown, the base of the first prism is opposite to the base of the middle section.
3. Effectively, the first two prisms (P and Q) act as a parallel glass slab which causes zero net deviation (only a lateral shift).
4. The final ray then passes through the third prism (R). Since the previous combination resulted in no angular deviation, the ray enters the last prism with the same relative orientation as it entered the first.
5. Consequently, the net deviation of the entire system remains equal to the deviation produced by a single prism. Step 3: Final Answer
The ray will suffer the same deviation as before.
23
PYQ 2026
medium
physicsID: bitsat-2
The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability for this wavelength, will be:
1
15°
2
30°
3
45°
4
60°
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept
The critical angle ( ) is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium (usually vacuum/air) is 90°. It depends on the refractive index of the medium. Step 2: Key Formula or Approach
1. Refractive index
2. Critical angle Step 3: Detailed Explanation
1. Calculate Refractive Index ( ):
Given and .
2. Calculate Critical Angle ( ):
Since , then . Step 4: Final Answer
The critical angle of the medium is 30°.
