Spherical Lenses

To solve the problem, we need to find the object distance for a concave mirror using the mirror formula.

1. Mirror Formula:

Where:
image distance = +30 cm (positive for real image on same side as object),
radius of curvature = 20 cm,
(negative for concave mirror)

2. Substituting into Mirror Formula:

Solving for :

3. Interpreting the Result:
The negative sign indicates the object is on the same side as the mirror, which is expected for a real object in mirror problems.

Final Answer:
The object distance is 7.5 cm (Option D).

To solve this problem, we need to determine how many positions of a convex lens will produce a sharp image on a screen, given that the distance between the object and the screen is more than four times the focal length of the lens.

1. Lens Formula:
The lens formula is: Where:
= focal length,
= image distance from the lens, and
= object distance from the lens.

2. Using Optical Bench Concept:
If the distance between the object and the screen (let's call it ) is fixed and , then there are exactly **two** positions of the convex lens where a sharp image can be formed on the screen.
These positions are symmetrical with respect to the center of the distance , and one gives a magnified image while the other gives a diminished image.

3. Condition for Two Positions:
Two positions for a sharp image are possible only if: This is given in the question, so the condition is satisfied.

Final Answer:
The correct answer is (B) 2.

To solve this question, we need to identify the type of mirror where both the object and its image lie on the same side of the mirror.

1. Mirror Types and Image Formation:
- Concave Mirror: Can form real or virtual images depending on the object distance. When the object is placed between the pole and the focus, the image is virtual, erect, and appears on the same side as the object.
- Convex Mirror: Always forms virtual, diminished, and erect images on the opposite side of the object.
- Plane Mirror: Always forms virtual images on the opposite side of the mirror.

2. Analyzing the Given Situation:
The question states that both the object and image lie on the same side of the mirror. This is possible only with a concave mirror when the object is placed very close (between pole and focus).

Final Answer:
Option (A) Concave is correct.

To solve this question, we need to identify the part of the human eye responsible for image formation.

1. Understanding Eye Anatomy and Function:
- Cornea: Transparent front part of the eye that helps in focusing light.
- Crystalline Lens: A transparent, flexible structure that fine-tunes the focus of light rays onto the retina, thus forming a clear image.
- Aqueous Humor: The fluid between cornea and lens, helps maintain pressure and provides nutrients, but not directly involved in image formation.
- Iris: Controls the size of the pupil to regulate light entry, not involved in focusing or image formation.

2. Identifying the Correct Answer:
The crystalline lens focuses light rays onto the retina and is directly responsible for image formation in the eye.

Final Answer:
Option (B) Crystalline lens is correct.

To solve this problem, we need to understand the reference point from which object distance ( ), image distance ( ), and focal length ( ) are measured in lens or mirror systems.

1. Standard Reference Point:
In the ray diagram for both mirrors and lenses, all distances (object distance, image distance, and focal length) are measured from a common point called the optic centre in case of lenses and the pole in case of mirrors.

2. Definitions:

• Object distance ( ) – Distance from the object to the optic centre.
• Image distance ( ) – Distance from the image to the optic centre.
• Focal length ( ) – Distance from the optic centre to the principal focus.

3. Evaluating the Options:

• (A) Focus (F) – Incorrect; it is the end point of focal length, not the reference.
• (B) Optic centre (P) – Correct; all distances are measured from here in a lens system.
• (C) Centre of curvature – Incorrect; mainly used in spherical mirrors.
• (D) Principal axis – Incorrect; it's a line, not a point of measurement.

Final Answer:
The correct answer is (B) Optic centre (P).

To solve the problem, we need to understand how a fish underwater perceives a bird flying vertically above the surface of water.

1. Concept of Refraction:
When light travels from air (rarer medium) to water (denser medium), it bends towards the normal. The reverse happens when looking from water to air—the apparent position of the object (here, the bird) appears to be further away than it actually is.

2. Applying the Concept:
The fish in the water observes the bird through the refracted rays. Due to refraction at the water-air interface, the bird appears to be at a higher position than it actually is, making it seem farther away.

Final Answer:
The fish sees the bird further away than actual distance (Option A).

To solve this question, we need to find the focal length of a plano-convex lens with refractive index and radius of curvature .

1. Lens Maker's Formula:
The general lens maker's formula for focal length is:

2. For a Plano-Convex Lens:
- One side is plane
- One side is convex
Now applying this to the formula:

3. Solving for :

Final Answer:
Option (D) is correct.

To solve this problem, we need to determine the object position when a convex lens forms an image at infinity.

1. Image at Infinity by Convex Lens:
A convex lens forms an image at infinity when the object is placed at the lens’s focus (F).

2. Behavior of Light Rays:
When parallel rays (like those from a distant object) pass through a convex lens, they converge at the focus. Conversely, if the object is at the focus, the refracted rays go parallel to the principal axis, appearing to meet at infinity—hence, the image forms at infinity.

3. Evaluating the Options:

• (A) Focus (F) – Correct ✔
• (B) – Incorrect; this forms an image at the same distance on the other side.
• (C) Infinity – Incorrect; object at infinity forms image at focus.
• (D) Pole (P) – Incorrect; not relevant to lenses, more to mirrors.

Final Answer:
The correct answer is (A) Focus (F).

To solve the problem, we need to understand the condition for the formation of a virtual image using a convex lens.

1. Understanding the Formation of Virtual Image:
For a convex lens, a virtual image is formed when the object is placed closer to the lens than its focal point (i.e., when the object distance is less than the focal length).

2. Conditions for Virtual Image:
When the object is placed at a distance less than the focal length ( ), the rays from the object diverge after passing through the lens, and the extended rays form a virtual image on the same side as the object.

Final Answer:
For a convex lens, magnification of the virtual image is possible only when the object distance is .

To solve the problem, we need to identify the correct form of the lens maker's formula.

1. Lens Maker's Formula:
The lens maker's formula relates the focal length of a lens to its refractive index and the radii of curvature of its two surfaces, and . The general form of the lens maker's formula is:

where: - is the refractive index of the material of the lens, - is the radius of curvature of the first surface, - is the radius of curvature of the second surface, - is the focal length of the lens.

2. Comparing with Given Options:
- Option (A) is correct as it matches the standard form of the lens maker's formula.

Final Answer:
The lens maker's formula is (Option A).