Question

A spherical mirror is to be used to form an image, five times as tall as an object, on a screen positioned 5.0 m from the mirror.

a)Describe the type of mirror required.  

____ whats its focal length??

b) Where should the mirror be positioned relative to the object?

the object should be ______?

Answer 1

Since the object is to be magnified, concave mirror has to be used. (Convex mirror can only form diminished images)

image distance, d_i = 5.0 m

Since the image is to be formed on a screen, it is real. So, h_i/h_o = -5

We have, 1/d_o + 1/d_i = 1/f

=> (d_i/d_o) + 1 = d_i/f

=> -(hi/h_o) + 1 = d_i/f

=> -(-5) + 1 = 5/f

=> 5/f = 6

=> f = 0.83 m

Now, d_i/d_o = -h_i/h_o = 5

=> d_o = d_i/5 = 5/5 = 1 m

So, the mirror should be positioned 1 m from the object.