Images Formed By Lenses

To find the mirror image of a clock time, subtract the given time from 12:00. Given time = 3:05

The correct answer is option (A): hr min

In a prism, the angle of deviation is minimum when the path of the light ray inside the prism is symmetric. This occurs when the angle of incidence is equal to the angle of emergence . At minimum deviation: This condition ensures that the ray passes through the prism symmetrically and the total deviation is minimized.

The correct answer is option (A):

Step 1: Recall the lens formula.

The lens formula is given by:

Rearranging for :

Simplify:

Step 2: Substitute the given values.

The focal length is . Substituting into the formula:

Final Answer: The image distance is , which corresponds to option .

Step 1: Understand the definition of paraxial rays.

Paraxial rays are light rays that travel very close to the principal axis of an optical system and make very small angles with it. By definition, the angle between paraxial rays and the principal axis is approximately .

Step 2: Analyze the options.

• (1) 45°: This is incorrect because paraxial rays do not make such a large angle with the principal axis.
• (2) 0°: This is correct because paraxial rays are nearly parallel to the principal axis.
• (3) 90°: This is incorrect because rays perpendicular to the principal axis are not paraxial.
• (4) 83°: This is incorrect because paraxial rays do not make such a large angle with the principal axis.

Final Answer: The angle between the paraxial rays and the principal axis is , which corresponds to option .

Step 1: Understand total internal reflection and its relation to the critical angle.

Total internal reflection occurs when light traveling through a denser medium (e.g., diamond) strikes the boundary with a less dense medium (e.g., air) at an angle greater than the critical angle. The critical angle ( ) depends on the refractive indices of the two media:

Diamond has a very high refractive index ( ), which results in a very low critical angle ( ). This low critical angle allows light to undergo multiple internal reflections within the diamond, making it shine brightly.

Step 2: Analyze the options.

• (1) Very high: The critical angle of diamond is not very high; it is very low. This option is incorrect.
• (2) Very low: This is correct because the high refractive index of diamond results in a very low critical angle.
• (3) Exactly 45°: The critical angle of diamond is much lower than . This option is incorrect.
• (4) None of these: This option is incorrect because the critical angle is indeed very low.

Final Answer: The critical angle of diamond is , which corresponds to option .

A magnifying lens is used to produce a magnified image of an object. To achieve this, the lens must cause rays of light to converge, forming a virtual, erect, and enlarged image when the object is placed within the focal length of the lens.

This behavior is exhibited by a convex lens, which is a converging lens. Out of the given options, both double convex and plano-convex lenses are convex lenses. However, the double convex lens is more commonly used as a magnifying glass because it has curvature on both sides, which increases its converging power.

Concave lenses (like double concave and plano-concave) are diverging lenses and cannot produce magnified virtual images as required for a magnifying lens.

Answer: Double convex

The focal plane is defined as the plane that passes through the focus of a lens or mirror and is perpendicular to the principal axis.

The principal axis is the straight line that passes through the center of curvature and the optical center (or pole) of the lens or mirror.

Since the focal plane contains all points where light rays parallel to the principal axis converge (in a converging system) or appear to diverge from (in a diverging system), it must be perpendicular to the axis along which the lens or mirror is aligned.

Answer: Perpendicular to the principal axis

Correct answer: focal length

Explanation:
In a lens, the focal length is the distance between the optic centre (the central point of the lens) and the focal point (the point where parallel rays of light converge or appear to diverge after passing through the lens).

This is a key parameter that determines the converging or diverging power of the lens.

Hence, the correct answer is: focal length.

Correct answer: a transparent material

Explanation:
A lens is an optical device that bends light rays by refraction. To allow light to pass through it and undergo refraction, a lens must be made of a transparent material.

Common materials used for making lenses include:
- Glass
- Plastic (such as acrylic or polycarbonate)
These materials are transparent and allow light to pass through them with minimal absorption.

Hence, the correct answer is: a transparent material.

Correct answer:

Explanation:
Snell's Law describes how light bends when it passes from one medium to another. It is mathematically expressed as: where:
- = angle of incidence
- = angle of refraction
- = refractive indices of the respective media
- = speeds of light in the respective media
This ratio remains constant for a given pair of media.

Hence, the correct answer is: .

In the case of myopia (nearsightedness), the image of distant objects is formed in front of the retina. This occurs because the eye is unable to focus light from distant objects correctly onto the retina. The image is formed too early, in front of the retina, leading to blurry vision for distant objects. Thus, the image in myopic defect is formed before the retina.

The correct option is (A): before the retina

When an object is placed between the focal point (F) and the optic center (O) of a convex lens, the image formed is virtual, erect, and magnified. This occurs because the light rays after passing through the lens diverge, and when extended backward, they appear to converge at a point behind the lens, forming a virtual image. Thus, the virtual image is formed between the focal point and the optic center. Therefore, the correct answer is: between the focal point and optic centre.

The correct option is (D): between focal point and optic centre

For a convex lens, the lens formula is given by: Where:
is the focal length,
is the image distance, and
is the object distance.
From the given data:
(object distance),
(image distance).
Substituting these values into the lens formula: Simplifying: Thus:

The correct option is (C):

In ray diagrams, the symbol ↕ typically represents a convex lens. This is because a convex lens is commonly used in optical ray diagrams, where the light rays converge to a focal point after passing through the lens. Thus, the correct answer is convex lens.

The correct option is (B): convex lens

In hypermetropia (also called farsightedness), the image of an object is formed behind the retina. This occurs because the focal point of the eye’s lens system falls behind the retina when the eye attempts to focus on nearby objects.

Concave lenses are diverging lenses, meaning they spread out parallel rays of light. When an object is placed in front of a concave lens, the rays of light coming from the object diverge after passing through the lens. These diverging rays appear to originate from a point closer to the lens than the actual object.

This is why the image formed is:

Virtual: The light rays do not actually converge to form the image. Instead, the image is formed by the apparent intersection of the diverging rays' extensions behind the lens.
Erect: The image is oriented in the same direction as the object.
Diminished: The image is smaller than the object. The position of the object only affects the size of the image, not its virtual and erect nature.

A convex lens forms a virtual image when the object is placed between the focal point (F) and the optic center (O) of the lens. In this situation, the image is virtual, erect, and magnified.

At infinity: A real, inverted, highly diminished image is formed at the focal point.
At the center of curvature (2F): A real, inverted, same-sized image is formed at the center of curvature on the other side.
Between the focal point (F) and the center of curvature (2F): A real, inverted, magnified image is formed beyond the center of curvature on the other side.