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# Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end of radius of curvature 10 cm. 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:60 cm70 cm80 cm90 cm

A
60 cm
B
80 cm
C
70 cm
D
90 cm
Solution
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#### Applying (μ2v−μ1u=μ2−μ1R) two times, we will get ⇒1v−1.5−50=1−1.5−10⇒1v=0.510−1.550=2.5−1.550⇒v=50.⇒AB=d, AI1=50cm BI1=(d−50)cmAgain, 1.5∞−1−(d−50)=1.5−110⇒1d−50=120⇒d=70cm.Hence, the answer is 70cm.

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