Question

If a swimming pool appears 6m deep, by what percentage is the apparent depth smaller than the true depth if its refractive index is 4/3

Answer 1

Answer:

25%

Explanation:

apparent depth = real depth/refractive index

6=rd / (4/3)

rd =6 x 4/3

rd =8m.

Answer 2

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Refractive index of a medium is the ratio of speed of light in air to speed of light in it. Mathematically represented as c / v.

Refraction is a phenomenon in which light ray travelling from a medium bends and twists its path due to density of media in which it is travelling.

Due to Refraction the depth of an object seems to change in comparison to it's actual depth in liquid media. Thus the depth of object due to refraction is called apparent depth.

Also Refractive Index of a medium is the ratio of real depth to apparent depth.

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We have been given that :-

• Apparent depth of pool :- 6m
• Real depth : - r = ?
• Refractive index of liquid in pool = (mu) =4/3
• By how much percent apparent depth is smaller than real depth = x = ?

Now we know :-

$\mu \: = \frac{real \: depth}{apparent \: depth}$

Putting the values :-

$\frac{4}{3} = \: \frac{r}{6} \\ \\ \frac{4 \times 6}{3} = r$

$\cancel \frac{24}{3} = r$

$r \: = \: 8m$

Now real depth of pool is 8m.

Now let's say apparent depth is x% smaller than real depth.

$\therefore \: x \: percent \: of \: 8 = 6$

$\frac{8x}{100} = 6$

$8x = 600$

$x = \frac{600}{8}$

$x = 7.5pc$

Therefore, the apparent depth of pool is 7.5% smaller than real depth.

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BY SCIVIBHANSHU

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