A rod of length 2 cm makes an angle 2 π 3 rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of 40 3 cm from the object as shown in the figure. The height of the image is 30 3 13 cm and the angle made by it with respect to the principal axis is rad. The value of α is π n rad , where n is
A. A
In convex lens, when an object is placed in between the centre of curvature and focus, the real image is formed behind the centre of curvature. The size of the image is larger than that of the object. Here, the angle made by inner side of rod with principal axis is π - 2 π 3 = π 3   rad . From figure, height of object is h o = 2 sin 60 ° = 2 × 3 2 = 3   cm and given height of image h i = 30 3 13   cm Size of object is u = 40 3 + 1 = 43 3   cm Now, using lens equation, 1 v - 1 - u = 1 f ⇒ v = f u f - u Image distance, O A ' = 40 3 × 10 43 3 - 10 = 40   cm And O B ' = 43 3 × 10 43 3 - 10 = 430 13   cm ∴   A ' B ' = 40 - 430 13 = 90 13   cm ∴   tan α = 30 3 13 × 90 13 = 1 3 ⇒   α = π 6 ∴   n = 6 . 00
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