A thin convex and concave lenses are kept in contact. The combination act as a convex lens of focal length 80 cm. If focal length of the convex lens is 20 cm, then power of the other lens is

The power of a lens is given by the formula P = 1/f, where f is the focal length of the lens. The focal length is usually measured in meters, so the power is measured in diopters (D).

Given that the combination of the two lenses acts as a single convex lens with a focal length of 80 cm (or 0.8 m), and the convex lens alone has a focal length of 20 cm (or 0.2 m), we can find the focal length of the concave lens.

1/f_total = 1/f1 + 1/f2

Where: f_total is the total focal length of the combination (0.8 m), f1 is the focal length of the convex lens (0.2 m), and f2 is the focal length of the concave lens, which we are trying to find.

Substituting the given values into the equation, we get:

1/0.8 = 1/0.2 + 1/f2

Solving for f2, we get:

f2 = 1 / [(1/0.8) - (1/0.2)] f2 = 1 / [1.25 - 5] f2 = 1 / -3.75 f2 = -0.267 m (or -26.7 cm)

The negative sign indicates that the lens is concave.

Now, we can find the power of the concave lens using the formula P = 1/f:

P = 1 / -0.267 P = -3.75 D

So, the power of the concave lens is -3.75 diopters.