Name: Applications of TIR: Mirage and Looming
Uploaded: 2019-07-19
Duration: 4 min 7 s
Description: Let’s learn about mirages and looming in this interesting video. These are fascinating phenomena of light observed on hot summer days.

Question

Explain why does a swimming pool appears shallower than it actually is. Obtain an expression for the normal displacement of an object immersed in water.

Accepted Answer

When an observer looks at the bottom of a swimming pool, the light rays falling on the retina of her eyes travel from the water into the air. Hence, the light travels from a denser medium into a rarer medium. The ray diagram for the above said situation is shown below:

$Chapter 4 Refraction of Light at Plane Surfaces - Concise Physics Part II - Selina Solutions for Class 10 Physics ICSE - TopperLearning$

Let O be a point at the bottom of the swimming pool. Light ray AO travels normally through the interface hence, it goes undeviated. The oblique ray OB will bend away from the normal as it enters into the air from water. It follows the path BC. Now I is the image of point O. Considering the $∠ i$ and $∠ r$ to be very small, in $∆ AOB$ and $△ AIB$ :

$\sin i = \tan i = \frac{A B}{A O}$ .......(i)

$\sin r = \tan r = \frac{A B}{A I}$ ......(ii)

As the light travels from water into the air, the refractive index of water with respect to air:

$n_{w a} = \frac{1}{n_{w a}} = \frac{\sin r}{\sin i} = \frac{AO}{AI}$ .......(iii)

Normal displacement of the object $= AO - AI$ ........(iv)

Using(iii) and (iv) we get:

$n_{w a} - 1 = \frac{A O - A I}{A I} = \frac{A O - A I}{A O} \times n_{w a}$

$\Rightarrow (A O - A I) = \frac{A O}{n_{w a}} (n_{w a} - 1)$

$\Rightarrow$ Normal displacement of an object $= AO (1 - \frac{1}{n_{wa}})$

Normal displacement of an object immersed in water= Real depth $\times (1 - \frac{1}{n_{wa}})$

Explain why does a swimming pool appears shallower than it actually is. Obtain an expression for the normal displacement of an object immersed in water.

Important Questions on Refraction of Light at a Plane Interface : Total Internal Reflection : Optical Fibre

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