Question

Obect is placed at a distance of 4cm from focus of concave mirror. The image is formed at a distance of 16cm from the focus on sameside. What is the focal length of the mirror ? Read question twice or thrice carefully and answer

Answer 1

Hola there,

Let Focal length (f) = x

According to the question,

Object distance (u) = -(x + 4) cm
Image distance (v) = -(x + 16) cm


Mirror formula => 1/u + 1/v = 1/f

=> -1/(x + 4) -1/(x + 16) = 1/x

=> [-(x + 16) -(x + 4)]x = (x + 4)(x + 16)

=> [- x - 16 - x - 4]x = (x² + 16x + 4x + 64]

=> [-2x - 20]x = (x² + 20x + 64)

=> -2x² - 20x = x² + 20x + 64

=> 3x² + 40x + 64 = 0

Now, we will solve this equation by quadratic formula.

Then we get,
=> x = (40+√832)/-6
= -11.474 

or:

=> x =(40 - √832)/-6
= -1.859 

So the focal length can be = -11.474 or -1.859


Hope this helps...:)