Identical objects are located at the same distance from two spherical mirrors, A

Question

Identical objects are located at the same distance from two spherical mirrors, A and B. The magnifications produced by the mirrors are mA = 4.16 and mB = 2.08. Calculate the ratio fA/fB of the focal lengths of the mirrors. Identical objects are located at the same distance from two spherical mirrors, A and B. The magnifications produced by the mirrors are mA = 4.16 and mB = 2.08. Calculate the ratio fA/fB of the focal lengths of the mirrors. Identical objects are located at the same distance from two spherical mirrors, A and B. The magnifications produced by the mirrors are mA = 4.16 and mB = 2.08. Calculate the ratio fA/fB of the focal lengths of the mirrors.

Explanation / Answer

u = object distance
v = image distance
f = focal length
m = magnification
Subscripts in square brackets identify the mirror.
Real is positive sign convention.

Both mirrors must be concave as m > 1 in both cases.

v[a] / u = 4.16
1 / 4.16u = 1 / v[a] ...(1)

v[b] / u =2.08

1 / u + 1 / v[a] = 1 / f[a]
1 / v[a] = 1 / f[a] - 1 / u

Using (1) to eliminate 1 / v[a]:
1 / f[a] - 1 / u = 1 / 4.16u
1 / f[a] = (1 + 1 / 4.16)u
= u

Similarly
1 / f[b] = (1 + 1 / 2.08)u
= 3u

f[a] / f[b] =
= 1.21.

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