CBSE Class 12 Physics 2014 Outside Delhi Set 2 Paper

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Question : 9
Total: 9
A convex lens of focal length 20‌cm is placed coaxially with a concave mirror of focal length 10‌cm at a distance of 50 apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.
Solution:  
The beem incident on lens L is parallel to principal axis. Hence, the lens forms an image I1 at its focus, i.e., at a distanec OI1=20‌cm from the lens.

The image I1 is formed in front of mirror and hence, acts as a real source for the mirror. The concave mirror forms the image I2, whose distance from the mirror can be calculated as,
‌
1
v
+‌
1
u
=‌
1
f

Here: u=−30‌cm, and f=−10‌cm
⇒‌
1
v
=‌
1
f
−‌
1
u

⇒‌
1
v
=−‌
1
10
+‌
1
30

⇒‌
1
v
=‌
1−3
30
=−‌
2
30

⇒v=−15‌cm
Hence, the final image is formed at a distance of 15‌cm from the concave mirror, as shown in the following figure.
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