An object of size 7 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At 54 cm from the mirror a screen is placed so that a sharp focused image can be obtained. The size and the nature of the image will be?

A
12 cm and inverted
B
14 cm and inverted
C
12 cm and real
D
14 cm and real

Solution:

An object of size

7 cm

is placed at

27 cm

in front of a Concave Mirror

of focal length

18 cm

. At

54 cm

from the mirror a screen is placed so that a sharp focused image can be obtained. The size and the nature of the image will be 14 cm and real.
Given,
Distance of the object from the mirror,

u = - 27 cm

(since it is a concave mirror)
The focal length (

f

) of the mirror,

f = - 18 cm

Height of the object

{, h}_{0} = 7 cm

Distance of the object from the mirror,

v = - 54 cm

m = \frac{h_{i}}{h_{o}}

\frac{h_{i}}{h_{o}} = - \frac{v}{u}

\frac{h_{i}}{7} = + \frac{54}{(- 27)}

h_{i} = - 2 \times 7

h_{i} = - 14 cm

The height of the image

(14 cm

) is double the size the height of the object (

7 cm

). Hence the nature of the image will be real and inverted.

An object of size $7 cm$ is placed at $27 cm$ in front of a concave mirror of focal length $18 cm$ . At $54 cm$ from the mirror a screen is placed so that a sharp focused image can be obtained. The size and the nature of the image will be?

Solution:

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