Question

A spherical mirror forms a real image five times the size of the object. This image is located 5m from the object (not from the lens).

a) Find the position of the object and the image

b) Find the focal length of the mirror

Answer 1

a)

1.25 m , 6.25 m

b)

1.04 m

Step-by-step explanation:

`h_(o)` = height of the object = h

`h_(i)` = height of the image = - 5 h

`d_(o)` = distance of the object from the mirror

`d_(i)` = distance of the image from the mirror =
`d_(o) + 5`

a)

Using the equation

`(h_(i))/(h_(o)) = (- d_(i))/(d_(o))`

`(- 5 h)/(h)} = (- (d_(o) + 5))/(d_(o))`

`d_(o)` = 1.25 m

`d_(i)` =
`1.25 + 5`

`d_(i)` = 6.25 m

b)

using the mirror equation

`(1)/(f) = (1)/(d_(o)) + (1)/(d_(i))`

`(1)/(f) = (1)/(1.25) + (1)/(6.25)`

`f` = 1.04 m