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Question

A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement (s) is (are) true?The refractive index of the lens is 2.5The radius of curvature of the convex surface is 45 cmThe faint image is erect and realThe focal length of the lens is 20 cm

A
The faint image is erect and real
B
The refractive index of the lens is 2.5
C
The focal length of the lens is 20 cm
D
The radius of curvature of the convex surface is 45 cm
Solution
Verified by Toppr

Case I,160+130=1f1f1=20cmCase II,110−130=1f2f2=15=R2R=30 cmFrom case I,f1=Rn−1=20Thus, n=2.5Radius of curvature is 30 cmFocal length of lens is f1=20 cmAnswer is option A and D.

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