A plano-convex glass (n = 1.5)lens has a curved side whose radius is 50 cm.If the image size is to be the same as the object size, the object should be placed at a distance from the lens of:
A)50 cm
B)100 cm
C)200 cm
D)340 cm
E)400 cm

Question

Quizplus · Accepted Answer

Since the image size is to be the same as the object size, we can assume that the magnification (M) is 1. Using the thin lens formula, we get:

1/f = (n - 1)(1/R1 - 1/R2)

where f is the focal length of the lens, n is the refractive index of the glass, R1 is the radius of curvature of the curved side, and R2 is the distance of the object or image from the lens. Since the lens is plano-convex, R1 is positive and R2 is negative (since the object and image are on opposite sides of the lens). Thus, we have:

1/f = (1.5 - 1)(1/50 - 1/R2)
1/f = (1/2)(1/50 - 1/R2)
1/f = (R2 - 50)/(100*R2)
f = 100*R2/(R2 - 50)

We know that M = -di/do, where di is the image distance and do is the object distance. Since M = 1, we have di = do. Also, since the lens is symmetrical, we can assume that the object and image distances are equal when the magnification is 1. Thus, we have:

do = di = 2*R2

Substituting this into the thin lens formula, we get:

1/f = (1.5 - 1)(1/50 - 1/(2*R2))
1/f = (1/2)(1/50 - 1/(2*R2))
1/f = (2*R2 - 50)/(200*R2)

Substituting the expression for f from above, we get:

(2*R2 - 50)/(200*R2) = 100*R2/(R2 - 50)

Solving for R2, we get:

R2 = 200 cm

Thus, the object should be placed at a distance of 200 cm from the lens. Therefore, the correct answer is C) 200 cm.

A Plano-Convex Glass (N = 1