Question

The relation between focal length F magnification m and image distance v of a spherical mirror of small aperture is given by

Answer 1

The relation between focal length f, magnification m and image distance v of a spherical mirror of small aperture is given by: m = (f-v) / f

- The thin lens formula is given as:

1/v - 1/u = 1/f

Multiplying both sides by v, we get:

1 - (v / u) = v/f

⇒ 1 - m = v/f  {Because for thin lens m = v/u}

⇒ m = 1 - v/f

⇒ m = (f-v) / f

- This is the required relation between f, m and v.

Answer 2

3: mf = v-f

Explanation:

We know that the formula of magnification m = v / u where v is the image distance and u is the object distance.

So u = v/m ------------(1)

Now the mirror formula is: 1/f  = 1/v + 1/u ----(2)

Substituting 1 in 2, we get:

1/f = 1/v + m/v

v = f (m+1)

 v = mf + f

 mf = v-f

Option 3 is the answer.