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.

Open in App

Solution

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:
$Now 1.33 = \frac{\sin 45 °}{\sin r} \Rightarrow \sin r = \frac{1}{1.33 \sqrt{2}} = 0.53 \Rightarrow \cos r = \sqrt{1 - \sin^{2} r} = \sqrt{1 - (0.53)^{2}} = 0.85 So, \tan r = 0.6235$

Therefore, shadow length of the pole = (0.5) $\times$ (1 + 0.6235) = 0.81175 m
= 81.2 cm

Suggest Corrections

Similar questions

Q. A

1 m

long rod is half dipped in a swimming pool. The sunlight is incident at

45^{\circ}

on the rod. Find the length of the shadow on the bed of swimming pool.

Q. A pile 4 m high stands in the lake, such that it appears 1 m above the surface of water . if refractive index of water is

μ = \frac{4}{3}

and sun rays make an angle of

45^{0}

with the water surface, then length of the shadow of pile on the bed of the lake will be:

A girl sees through a circular glass slab(refractive index 1.50 of thickness 20 mm and diameter 60 cm to the bottom of a swimming pol. Refractive index of water is 1.33. The bottom surface of the slab is in contact with the water surface.

The depth of swimming pool is 6m. The area of bottom of swimming pool that can be seen through the slab is approximately.

Q. A pole

4 m

high driven into bottom of a lake is

1 m

above the water. If the incident sun rays make an angle of

53^{\circ}

with the normal at water surface, then the length of the shadow of the pile on the bottom of the lake will be

[

Given refractive index of water

= \frac{4}{3}]

Q. A girl sees through a circular glass slab(refractive index

1.50

of thickness

20 m m

and diameter

60 c m

to the bottom of a swimming pol. Refractive index of water is

1.33

. The bottom surface of the slab is in contact with the water surface.
The depth of swimming pool is

6 m

. The area of bottom of swimming pool that can be seen through the slab is approximately.

Join BYJU'S Learning Program