Answer to Question #90505 in Optics for Sukritha p

Question

An object is placed at a distance of 100cm from a convex mirror, the magnification produced is half. Where the object should be placed to a magnification of 1/4

Answer 1

We can writer for a convex mirror

$$\frac {1}{d}-\frac {1}{d_i}=-\frac {1}{F} (1)$$

The magnification of a convex mirror is equal to

$$k = \frac {d_i}{d} (2)$$

Using (2) we get:

$$d_i=kd (3)$$

We put (3) in (1):

$$\frac {1}{d}-\frac {1}{ kd }=-\frac {1}{F} (4)$$

In the first case, we have: d=100 cm, k=0.5

Using (4) we get: d=F

In the second case, we have: F=100 cm

Using (4) we get: d=300 cm

Answer

300 cm