A planoconvex lens is located 15 cm to the right of a small bright object, locat

Question

A planoconvex lens is located 15 cm to the right of a small bright object, located on the axis of the lens, as shown in the diagram below. There is a plane mirror located to the right of the lens, which makes an angle of 90 degree with the axis of the lens. The combination of the lens and the plane mirror results in an image being formed exactly at the same place as the object. Explain why this means that the object must be located at the focal point of the lens. You are advised to use a ray diagram to assist your explanation. Assume that the lens is thin. The glass of the planoconvex lens has a refractive index of 1.6. Calculate the radius of curvature of the curved surface of the planoconvex lens.

Explanation / Answer

i) If the object is placed at focal point of lens , it will form an image on right side of plane mirror, so, the resulting image formed from the mirror and lens combination is at the same place as the object .

ii)   Here, 1/f = (n - 1) * (1/R1 - 1/R2)

=>    1/15 = (1.6 - 1)(1/R1 - 0)

=>     R1 = 9 cm

=> radius of curvature of curved surface = 9 cm

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