Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end of radius of curvature 10cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S1 on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S2. The distance d is
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u1 = –50 cm
n1 = 1.5
n2 = 1
R = –10
So,
v1 = 50 cm
For S2
u = – (d – 50); n1 = 1; n2 = 1.5; v = ; R = +10
d – 50 = 20
So, d = 70 cm
If
u = +(50 – d)
n1 = 1; n2 = 1.5; v = ; R = +0
So, 50 – d = 20
d = 50 – 20 = 30 cm