Question

the distance of an object from the focus of a convex mirror of radius of curvature 'a' is 'b'. find distance of image from focus?

Answer 1

First we need to calculate some values such as “b” is a distance and it could be measured either as (Do - f), or as (f - Do)

b = Do - f

Then: a = Di - f

f^2 = (a) (b)

Plugging in we obtain: (R/2)^2 = a b → a = f^2 / b

Check: let R = 12 cm; then f = 6 cm, Let b = 3 cm; then Do = 9 cm.

And if we use the mirror equation then: 1/f = 1/Do + 1/Di and solve for Di

Di = 18 cm

a = 18 - 6 = 12 cm

f^2 = 6 * 6 = 36; a * b = 12 * 3 = 36

And now we know that if Do = 2 cm; then b = 6 - 2 = 4 cm

Use the formula and we get Di = - 3 cm

Then the distance between the virtual image and the focus is: 3 + 6 = 9 cm

f^2 = 6^2 = 36 [a * b = 4 * 6 = 36]