Question

A pole of length 1.00 m stands half dipped in a swimming pool with water level 50.0 cm higher than the bed. The refractive index of water is 1.33 and sunlight is coming at an angle of 45° with the vertical. Find the length of the shadow of the pole on the bed.

Answer 1

Given,
Length of the pole = 1.00 m
Water level of the swimming pool is 50.0 cm higher than the bed.
Refractive index (μ) of water = 1.33

According to the figure, shadow length = BA' = BD + DA'= 0.5 + 0.5 tan r
Using Snell's law:

\[Now  1 . 33 = \frac{\sin  45^\circ }{\sin  r}\] 

\[ \Rightarrow   \sin  r = \frac{1}{1 . 33\sqrt{2}} = 0 . 53\] 

\[ \Rightarrow   \cos  r = \sqrt{1 -\sin^2 r}\] 

\[ = \sqrt{1 - (0 . 53 )^2} = 0 . 85\] 

\[So,   \tan  r = 0 . 6235\] 
Therefore, shadow length of the pole  = (0.5)
\[\times\] (1 + 0.6235) = 0.81175 m
= 81.2 cm