Question

How far should an object be placed from a concave spherical mirror of radius
38cm to form a real image of one-ninth its size?

Answer 1

Question:

How far should an object be placed from a concave spherical mirror of radius 38cm to form a real image of one-ninth its size?

Solution:

If radius of spherical mirror is $R = 38\,\mathrm{sm}$ then focal length of mirror is

$$F = R / 2 = 19\,\mathrm{cm}$$

Because we have real image of one-ninth its size we get the object's position as $S > 2^*F$,

We have $D / S = m$, $D = S^*m$ (here $m = 1/9$ is the magnification, $D$ is image position) and

$$1 / S + 1 / D = 1 / F$$

So, we arrive at

$$\frac{1}{S} \left(1 + \frac{1}{m}\right) = \frac{1}{F}$$

And substituting values we get the answer:

$$S = F \frac{m + 1}{m} \approx 21\,\mathrm{sm}$$