Question

a certain projetor uses a concave mirror for projecting an object's image on a screen .it produces on image that is 4 times bigger than the object and the screen is 5 m away from the mirror as shown in fig 5.2, calculate the focal length of the mirror.​

Answer 1

f = 1 m

Step-by-step explanation:

The magnification of the lens is given by the formula:

`M = (q)/(p)`

where,

M = Magnification = 4

q = image distance = 5 m

p = object distance = ?

Therefore,

`4 = (5\ m)/(p)\\\\p = (5\ m)/(4)\\\\p = 1.25\ m`

Now using thin lens formula:

`(1)/(f)=(1)/(p)+(1)/(q)\\\\(1)/(f) = (1)/(1.25\ m)+(1)/(5\ m)\\\\(1)/(f) = 1\ m^(-1)\\\\`

f = 1 m