The image of an object formed by a mirror is real, inverted and is of magnification -1. If the image is at the distance of 30 cm from the mirror, where is the object placed? Find the position of the image if the object is now moved 20 cm towards the mirror. What is the nature of the image obtained? Justify your answer with the help of a ray diagram.

OR

What is meant by the power of a lens? You have three lenses L₁, L₂ and L₃ of powers + 10D, + 5D and -10D respectively. State the nature and focal length of each lens. Explain which of the three lenses will form a virtual and magnified image of an object placed at 15 cm from the lens. Draw the ray diagram in support of your answer.

Given:

Magnification of mirror = -1

The distance of image from mirror = 30 cm

Distance moved towards the mirror = 20 cm

To find: Position of image

The ray diagram is given below:

Magnification,

u = 30 cm

Now by the mirror formula,

u = - 30 cm and v = - 30 cm.

f = -15

Now since the image is moved 20 cm towards the mirror, new u = -30 + 20

= -10 cm

So, a new position can be determined as follows:

v = 30 cm

So the new position of the image is at 30 cm from the mirror.

OR

Given:

Power of Lens L₁, P₁ = + 10D

Power of Lens L₂, P₂ = + 5D

Power of Lens L₃, P₃ = -10D

To find: Focal length of the lenses

Solution:

= + 10 cm

Now after noticing the power of the given lenses it can be concluded that lens L₁ and L₂ have positive power and hence they are convex lenses. Power of lens L₃ is negative, and hence lens L₃ is a concave lens.

Convex lenses only have the property to form the virtual and magnified image of the object placed at the optical centre or principal focus of the lens. The concave lens does not form a virtual or magnified image of an object at all.