Question

When an object is placed at a distance of 50 cm from a convex lens, an image of same size as the object is formed. What will be the nature of the image formed when the object is placed at a distance :

a) 20 cm from the lens

b) 30 cm from the lens

Explain your answer with reason. Also, calculate the distance of the image in each case.

Answer 1

Image is formed of the same size so
50cm = 2f
So focal length = 50/2 = 25 cm
f = 25cm

a. Image formed will be virtual .
Erect .
Larger than the object.
1/v - 1/u = 1/f
1/v = 1/25 + 1/-20
1/v = 4/100 - 5/100
1/v = -1/100
v = -100 cm

b. Image formed will be larger than the object.
Image formed will be real.
Image will be formed beyond 2F on the right side of the lens.
1/v = 1/u + 1/f
1/v = 1/-30 + 1/25
1/v = 5/-150 + 6/150
1/v = -5/150 + 6/150
1/v = 1/150
v = 150cm

Answer 2

Answer:

When an object is placed at a distance of 50 cm from a convex lens, an image of same size as the object is formed. What will be the nature of the image formed when the object is placed at a distance :

a) 20 cm from the lens

b) 30 cm from the lens