Question

A beaded screen (Fig.) returns light back to the source if light focuses on its back surface. For use by skindivers in water (n =$\frac { 4 } { 3 }$), of what index material should the beads be made ideally?

• A. $\frac { 3 } { 2 }$
• B. $\frac { 4 } { 3 }$
• C. $\frac { 5 } { 4 }$
• D. $\frac { 8 } { 3 }$

Answer 1

Answer: (D)

$\frac { 8 } { 3 }$

Answer 2

Let the required index of refraction be 'n', (see Fig. (2)).

Fig. (2)

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 i₂ = n sin i₁ for small angles i₁ and i₂ becomes n' i₂ = ni₁. As i₃ = i₁, i₃ = 2i₂, we have i₁ = 2i₂. Therefore, n' = 2n = $\frac { 8 } { 3 }$ .