A beaded screen (Fig.) returns light back to the source if light focuses on its back surface. For use by skindivers in water (n = 
), of what index material should the beads be made ideally?
Text Solution
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Let the required index of refraction be 'n', (see Fig. ).
Fig.
If a pencil of paraxial rays which are parallel to the axis, OP, strikes at P, the reflected rays will return back parallel to OP. Snell's law of refraction n' sin i 2 = n sin i 1 for small angles i 1 and i 2 becomes n' i 2 = ni 1 . As i 3 = i 1 , i 3 = 2i 2 , we have i 1 = 2i 2 . Therefore, n' = 2n = 
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