Question

I really would appreciate a quick response!

Q) Use the mirror equation to show that

a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f

b)a convex mirror always produces a virtual image independant of the location of the object.

c) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

Answer 1

Mirror equation is,

1/f = 1/v + 1/u

(a)

(a) For a concave mirror, the focal length ( f ) is negative.

therefore, f < 0

When the object is placed on the left side of the mirror, the object distance ( u ) is negative.

Therefore, u < 0

For image distance v , we can write the lens formula as:

Sp, 1/v -1/u = 1/f

1/v = 1/f - 1/u ....(i)

The object lies between f and 2 f

Therefore, 2f < u < f

1/2f > 1/u > 1/f

-1/2f < -1/u < -1/f

1/f - 1/2f < 1/f - 1/u < 0

(u and f are -ve)

Using equation (i),

1/2f < 1/v < 0

1/v is negative, v is negative.

1/2f < 1/v

2f > v

-v > -2f

Therefore, the image lies beyond 2f.

In the same way solve for the other parts.