An object of size 7.0 cm is placed at a distance of 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a sharp focussed image can be obtained? Find the size and nature of the i...
An object of size 7.0 cm is placed at a distance of 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed so that a sharp focussed image can be obtained? Find the size and nature of the image.
Given: h_{1} = 7 cm, u = 27 cm, f = 18 cm, v = ?
Applying the formula \(\frac{1}{f}\) = \(\frac{1}{v}\) + \(\frac{1}{u}\)
we get,
\(\frac{1}{18}\) = \(\frac{1}{v}\) + \(\frac{1}{27}\)
⇒ \(\frac{1}{18}\) + \(\frac{1}{27}\) = \(\frac{1}{v}\)
⇒ \(\frac{3 + 2}{54}\) = \(\frac{1}{v}\)
⇒ \(\frac{1}{54}\) = \(\frac{1}{v}\)
⇒ v = 54 cm
Hence, the screen should be placed at a distance of 54 cm from the mirror.
Now, applying the formula m = \(\frac{v}{u}\) = \(\frac{h_2}{h_1}\),
we get
⇒ \(\frac{(54)}{27}\) = \(\frac{h_2}{7}\)
⇒ h_{2} = 2 x 7 = 14 cm
∴ Size of the image is 14 cm.
Nature of image: Negative sign shows that the image is inverted and enlarged.

What is meant by power of accommodation of the eye?
3 years ago

A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?
3 years ago

Find the focal length of a lens of power 2.0 D. What type of lens is this?
3 years ago

An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.
3 years ago

The magnification produced by a plane mirror is +1. What does this mean?
3 years ago
 321 Forums
 27.3 K Topics
 53.8 K Posts
 2 Online
 12.4 K Members