Question

A concave mirror of focal length 10cm and a convex mirror of focal length 15 cm are placed facing each other 40 cm apart. A point object is placed between the mirrors, on their common axis and 15 cm from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror h​

Answer 1

Answer:

Given –

• The focal length of concave mirror is 10 cm.
• The focal length of convex mirror is 15 cm.
• The mirrors are kept at a distance of 40 cm from each other.
• A point sized object.
• The object is placed 15 cm away from concave mirror.

To Find –

• Position of the image and nature of the image ?

Solution –

Mirror formula : 1/v + 1/u = 1/f.

In concave mirror,

➸ 1/v + 1/-10 = 1/-15

➸ 1/v = -1/15 + 1/10

➸ 1/v = (10-15)/150

➸ 1/v = -5/150

➸ 1/v = -1/30

➸ v = -30 cm

Image is 30 cm in front of the mirror. It is real and inverted.

Now, the image formed by concave mirror will be the object for convex mirror.

Hence, the Object distance = 10 cm.

In convex mirror,

➸ 1/v + 1/-10 = 1/15

➸ 1/v = 1/15 + 1/10

➸ 1/v = (10 + 15)/150

➸ 1/v = 25/150

➸ 1/v = 5/30

➸ 1/v = 1/6

➸ v = 6 cm

Hence, image is formed 6 cm away behind the mirror.

The image is virtual and erect.