Question:

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it;

Updated On: Jun 7, 2022
  • 30cm
  • 60cm
  • 50cm
  • 12cm
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The Correct Option is C

Solution and Explanation

Using the formula $ \frac{1}{\upsilon }-\frac{1}{u}=\frac{1}{f} $ $ \frac{1}{v}-\frac{1}{-30}=\frac{1}{20} $ $ \upsilon =60\,cm $ If the image is formed at the centre of curvature of the mirror, the coincidence is possible. Then the rays refracting through the lens will fall normally on the convex mirror and retrace their path to form the image at O. Hence, the distance between lens and mirror will be = 60 - 10 = 50 cm.
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Concepts Used:

Ray Optics and Optical Instruments

Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.

Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.

Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.

Speed of light is the rate at which the light travels in free space.

A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.

Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.

Read More: Ray Optics and Optical Instruments