The arrangement shown given that a biconvex lens of radius of curvature equal to 10 cm and concave mirror of focal length equal to 20 CM then find the distance x such that the final image formed by the system concerned with the object?

Question

Answer

Problem:
The arrangement shown given that a biconvex lens of radius of curvature equal to 10 cm and concave mirror of focal length equal to 20 CM then find the distance x such that the final image formed by the system concerned with the object?

Solution:

Given:

Radius of curvature of biconvex lens, R = 10 cm

Focal length of concave mirror, f = -20 cm

Formula:

For a thin lens, the lens formula is given by 1/f = 1/v - 1/u, where f is the focal length of the lens, u is the distance of the object from the lens and v is the distance of the image from the lens.

For a spherical mirror, the mirror formula is given by 1/f = 1/v + 1/u, where f is the focal length of the mirror, u is the distance of the object from the mirror and v is the distance of the image from the mirror.

Analysis:

The biconvex lens will form an image of the object at a distance v1 from the lens.

This image will act as the object for the concave mirror.

The concave mirror will form the final image at a distance v2 from the mirror.

The distance of the object from the biconvex lens is u = x.

Calculation:

Using the lens formula for the biconvex lens, we get 1/f = 1/v1 - 1/u = 1/v1 - 1/x.

Using the mirror formula for the concave mirror, we get 1/f = 1/v2 + 1/v1.

Substituting f = -20 cm and solving the two equations, we get v1 = -30 cm and v2 = -60 cm.

The negative sign indicates that the image formed is virtual.

Therefore, the final image is formed at a distance of x + v2 = x - 60 cm from the object.

Answer:
The distance x such that the final image formed by the system concerned with the object is x - 60 cm.

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