Question

A meter stick lies along the optic axis of a convex lens of focal length 40 cm its nearer end 60 cm from the mirror surface. How long is the image of stick?

A. 200cm
B. 2003cm
C. 8cm
D. 2106cm

Answer 1

To find the image length, the image distances for both ends of the stick placed along the optic axis of the convex lens are calculated using the lens formula. The correct length of the image of the stick is therefore 8cm, which corresponds to option C.

Step-by-step explanation:

To calculate the length of the image of the stick formed by the convex lens, we need to determine the image distances for both ends of the stick. The stick is placed along the optic axis with its nearer end 60cm from the convex lens of focal length 40cm.

Using the lens formula: 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance. For the first end of the stick (nearer end):

1. Substitute the values into the lens formula: 1/40 = 1/v - 1/(-60).
2. Solve for v: 1/v = 1/40 + 1/60, giving v = 24 cm (image distance for the nearer end).

Since the stick is 1m long, the farther end is 60cm + 100cm = 160cm from the lens. Repeat the calculations for the farther end:

1. Substitute the values into the lens formula: 1/40 = 1/v - 1/(-160).
2. Solve for v: 1/v = 1/40 + 1/160, giving v = 32 cm (image distance for the farther end).
3. Subtracting the image distance for the nearer end from that of the farther end gives the length of the image as 8cm.

Now, we subtract the image distance of the nearer end from that of the farther end to find the length of the image: 32cm - 24cm = 8cm.