Optics

Step 1: Image formation by the convex lens

When an object is at infinity, a convex lens forms its image at its focal point.

Given focal length of the convex lens cm.

Size of the image formed by the convex lens cm.

The distance of this image from the convex lens is cm.

Step 2: Object for the concave lens

A concave lens of focal length cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens.

The image formed by the convex lens acts as the object for the concave lens.

The object distance for the concave lens ( ) is the distance between the image formed by the convex lens and the concave lens.

cm.

Since the object is to the left of the concave lens (in the direction of light travel from convex lens image), is positive according to sign convention used in lens formula.

Step 3: Image distance for the concave lens

Using the lens formula for the concave lens:

cm.

The image is formed at a distance of 5 cm from the concave lens, and it is positive, meaning it is on the right side of the concave lens (same side as the refracted light).

Step 4: Magnification by the concave lens

Magnification produced by the concave lens is .

Step 5: Size of the final image

The size of the image formed by the convex lens is the object size for the concave lens, so cm.

The size of the final image formed by the concave lens is cm.

Final Answer: The final answer is

The power ( ) of a lens is the reciprocal of its focal length ( ): . When two thin lenses are in contact, the total power is the sum of their individual powers: . A biconcave lens has a negative focal length.

Let:

Case 1: Two biconvex lenses in contact:

Case 2: First convex lens and biconcave lens in contact:

Case 3: Second convex lens and biconcave lens in contact:

We can express these as:

, and The correct answer is (D) .

Step 1: Lens Maker's Formula
The formula is:

where:

- is the focal length of the lens
- is the refractive index of the lens material
- is the refractive index of the surrounding medium
- and are the radii of curvature of the lens surfaces

Step 2: Apply Lens Maker's Formula for lens in air

For a glass lens in air, let be the focal length.

The refractive index of glass with respect to air is given as .

Here, and (approximately).

Step 3: Apply Lens Maker's Formula for lens in water

For a glass lens in water, let be the focal length.

The refractive index of glass with respect to water is needed. We are given the refractive index of air to glass ( ) and air to water ( ). The refractive index of glass with respect to water ( ) is given by:

Here, and , or directly use as the refractive index of lens material with respect to surrounding medium (water).

Step 4: Find the ratio of focal lengths

Divide the equation for by the equation for :

Therefore, the ratio of focal lengths of a glass lens in water and in air is .

Final Answer: The final answer is