An object 50 cm tall is placed on the principal axis of a convex lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens upto two places of decimal.

To calculate the focal length of the lens, we can use the lens formula:

1/f = 1/v - 1/u

Where: f is the focal length of the lens, v is the image distance from the lens, and u is the object distance from the lens.

Given: Object height (h) = 50 cm Image height (h') = 20 cm Image distance (v) = 10 cm

First, we need to find the object distance (u). We can use the magnification formula:

m = -v/u

Where: m is the magnification of the lens.

Given: h' = -m * h

Substituting the given values: 20 cm = -m * 50 cm

Solving for m: m = -20 cm / 50 cm m = -0.4

Now, we can find the object distance (u) using the magnification formula: -0.4 = -10 cm / u

Solving for u: u = 10 cm / 0.4 u = 25 cm

Now, we can substitute the values of u, v, and h' into the lens formula to find the focal length (f):

1/f = 1/v - 1/u 1/f = 1/10 cm - 1/25 cm

Simplifying the equation: 1/f = (25 - 10) / (10 * 25) 1/f = 15 / 250 1/f = 0.06

Taking the reciprocal of both sides: f = 1 / 0.06 f = 16.67 cm

Therefore, the focal length of the lens is approximately 16.67 cm.