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Ray Optics and Optical Instruments

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The figure shows an arrangement of an equi-convex lens and a c

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Hard

Solving time: 5 mins

The figure shows an arrangement of an equi-convex lens and a concave mirror. A point object $O$ is placed on the principal axis at a distance $40 cm$ from the lens such that the final image is also formed at the position of the object. If the radius of curvature of the concave mirror is $80 cm$ , find the distance $d$ . Also, draw the ray diagram. The focal length of the lens in air is $20 cm$ .

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Book:

Optics And Modern Physics (DC Pandey)

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The figure shows an arrangement of an equi-convex lens and a concave mirror. A point object

O

is placed on the principal axis at a distance

40 cm

from the lens such that the final image is also formed at the position of the object. If the radius of curvature of the concave mirror is

80 cm

, find the distance

d

. Also, draw the ray diagram. The focal length of the lens in air is

20 cm

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

\frac{1}{20} = (1.5 - 1) (\frac{1}{R} - \frac{1}{- R}) ∴ R = 20 cm

Applying

\frac{μ _{2}}{v} - \frac{μ _{1}}{u} = \frac{μ _{2} - μ _{1}}{R}

twice with the condition that rays must fall normally on the concave mirror.

\frac{1.5}{v _{1}} - \frac{1.2}{- 40} = \frac{1.5 - 1.2}{+ 20} \frac{2.0}{d - 80} - \frac{1.5}{v _{1}} = \frac{2.0 - 1.5}{- 20}

Solving Eqs. (i) and (ii), we get

d = 30 cm

and

v_{1} = - 100 cm

The ray diagram is as shown in figure.
Solution Image

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Question Text	The figure shows an arrangement of an equi-convex lens and a concave mirror. A point object $O$ is placed on the principal axis at a distance $40 cm$ from the lens such that the final image is also formed at the position of the object. If the radius of curvature of the concave mirror is $80 cm$ , find the distance $d$ . Also, draw the ray diagram. The focal length of the lens in air is $20 cm$ .
Topic	Ray Optics and Optical Instruments
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	83

Text solutionVerified

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