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Question
A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.
Solution
Given:
Convex lens of focal length (fl) = 15 cm
Concave mirror of focal length (f2) = 10 cm
Distance between the lens and the mirror = 50 cm
Point source is placed at a distance of 40 cm from the lens.
It means the point source is at the focus of the mirror.
Thus, two images will be formed:
(a) One due to direct transmission of light through the lens.
(b) One due to reflection and then transmission of the rays through the lens.
Case 1:
(S') For the image by direct transmission, we have:
Object distance (u) = − 40 cm
fl = 15 cm
Using the lens formula, we get:
\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]
\[\Rightarrow\frac{1}{v}=\frac{1}{15}+\frac{1}{( - 40)}\]
\[=\frac{40 - 15}{40 \times 15}\]
\[\Rightarrow v=\frac{40 \times 15}{40 - 15}\]
Therefore, v is 24 cm to the left from the lens.
Case II:
(S') Since the object is placed at the focus of the mirror, the rays become parallel to the lens after reflection.
∴ Object distance (u) = ∞ ⇒ fl = 15 cm
\[\Rightarrow \frac{1}{v} - \frac{1}{u} = \frac{1}{15}\]
Thus, v is 15 cm to the left of the lens.
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