Answer to Question #90505 in Optics for Sukritha p

Question #90505
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
1
Expert's answer
2019-06-04T12:28:01-0400

We can writer for a convex mirror

1d1di=1F(1)\frac {1}{d}-\frac {1}{d_i}=-\frac {1}{F} (1)

The magnification of a convex mirror is equal to


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

Using (2) we get:


di=kd(3)d_i=kd (3)

We put (3) in (1):


1d1kd=1F(4)\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


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