Question

A nail is placed at the bottom of a bucket which is filled with water to a depth of 20cm . At what depth will the nail appear to be viewed from the top.(refractive index of water = 1.33)

Answer 1

Answer: 15 cm

Explanation: When we view from rare to denser medium , apparent length will be shortened.

H' = H / refractive index

H ' = 20/ 1.33 = 15 cm

You can write 1.33 = 4/3

Answer 2

Answer: The nail will appear at a depth of 15.037 cm from the top.

Given: Water filled 20 cm.

To Find: Depth the nail appear.

Step-by-step explanation:

Step 1: When an object is placed in a medium and an observer see that object from rarer medium then it's apparent height is less than the real height. The apparent height of the object is totally depend upon the refractive index of the medium.

Step 2: When light enters a substance, its refractive index influences how much of its path is bent. Snell's rule of refraction, which states that $n_1 sin \theta_1 = n_2 sin \theta_2$, describes this. Here, $\theta_1$ and $\theta_2$ represent, respectively, the angle of incidence and angle of refraction of a ray as it crosses the boundary between two media with refractive indices of $n_1$ and $n_2$, and $n_1$ and $n_1$ are the media. In addition to determining the critical angle for total internal reflection, their intensity (Fresnel's equations), and Brewster's angle, the refractive indices also control how much light is reflected when it reaches the interface.

Step 3:

$\frac{\text{real depth}}{\text{apparent depth}}=\frac{h}{h'}= n$

Since, real depth = 20 cm and refractive index of water = 1.33

Apparent depth = real depth / refractive index of water

Apparent depth = 20/1.33 = 15.037 cm

The nail will appear at a depth of 15.037 cm from the top.

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