Q. 14.5( 128 Votes )

# A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

Answer :

Given,

Size of the candle, *h* = 2.5 cm

Object distance, *u* = –27 cm

Image size = *h*’ = ?

Radius of curvature of the concave mirror,

*R* = – 36 cm

Now focal length f is given as f = R/2

∴ f = R/2 = -18 cm

The image distance can be obtained using the mirror equation,

Where,

f is the focal length

u is object distance and

v is the image distance

⇒

⇒

⇒

⇒ v = -54 cm

Therefore, the screen should be placed at a distance of 54 cm

from the mirror to obtain a sharp image.

The magnification is given by

Where,

m is the magnification

h’ is the height of the image

h is the height of the object

v is the image distance

u is the object distance

Using the equation, we get,

⇒

⇒ h^{’} = -5 cm

∴ The height of the image is 5cm. The negative sign indicate that the image is real, inverted and magnified.

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