 Math »
 A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index..?
A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index..?
Explore the depths of physics: uncover the refractive index of water. From a tank filled to 12.5 cm, gauge the needle's apparent depth at 9.4 cm to reveal its optical properties.
by Maivizhi A
Updated Mar 18, 2024
A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 upto the same height, by what distance would be microscope have to be moved to focus on the needle again?
The microscope needs to be moved by approximately 1.73 cm to focus on the needle again.
To find the refractive index of water, we can use the apparent depth formula:
n_1/n_2 = d_real/d_apparent
Where:
 n_1 = Refractive index of the medium above the water (usually air, so n_1 = 1)
 n_2 = Refractive index of water
 d_real = Real depth of the needle (needle's actual depth in water)
 d_apparent = Apparent depth of the needle (as observed through the microscope)
Given:
 d_real = 12.5 cm
 d_apparent = 9.4 cm
 n_1 = 1
We can rearrange the formula to solve for n_2:
n_2 = (d_real/d_apparent) * n_1
n_2 = (12.5/9.4) * 1
n_2 ≈ 1.33
So, the refractive index of water is approximately 1.33.
Now, when water is replaced by a liquid of refractive index 1.63, the apparent depth of the needle will change. We can use a similar formula to find the new apparent depth, and then calculate the distance by which the microscope must be moved.
Let's denote the new apparent depth as d_apparent_new. We'll also denote the distance by which the microscope has to be moved as x.
d_apparent_new = (n_1/n_new) * d_real
Given:
 n_1 = 1
 n_new = 1.63
 d_real = 12.5 cm
d_apparent_new = (1/1.63) * 12.5
d_apparent_new ≈ 7.67 cm
Now, to find the distance x by which the microscope needs to be moved, we'll take the difference between the original apparent depth and the new apparent depth:
x = d_apparent  d_apparent_new
x = 9.4  7.67
x ≈ 1.73 cm
So, the microscope needs to be moved by approximately 1.73 cm to focus on the needle again.
Refraction of Light
Refraction of light is a phenomenon that occurs when light waves pass from one medium into another with a different optical density. Optical density is a measure of how much the material slows down the speed of light compared to its speed in a vacuum. When light passes through a medium such as air, water, glass, or any other transparent substance, it may change direction, or bend, due to the change in speed caused by the change in medium.
The bending of light during refraction can be understood through Snell's Law, which states:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
 n1 and n2 are the refractive indices of the two media.
 theta1 and theta2 are the angles that the incident ray and the refracted ray make with the normal (an imaginary line perpendicular to the surface at the point of incidence).
Key points about refraction:

Change in speed: Light waves travel at different speeds in different materials due to differences in optical density. When light enters a denser medium, it slows down, causing it to bend towards the normal. When it exits to a less dense medium, it speeds up and bends away from the normal.

Change in wavelength: Refraction doesn't change the frequency of light but can change its wavelength. As light enters a denser medium, its wavelength decreases, while in a less dense medium, its wavelength increases.

Critical angle: If the angle of incidence is increased beyond a certain critical angle, the refracted ray will be bent so much that it travels along the boundary between the two media. This phenomenon is called total internal reflection and is the basis for optical fibers and mirages.

Dispersion: Different colors of light bend by different amounts when they pass through a prism due to differences in their wavelengths. This separation of colors is called dispersion and is responsible for the formation of rainbows and the color spectrum seen in a prism.
Refraction plays a crucial role in various optical devices and natural phenomena, from lenses and prisms to the behavior of light in the atmosphere, oceans, and other transparent media.
A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm  FAQs
1. What is refraction of light?
Refraction of light is the bending of light waves when they pass from one medium to another due to a change in optical density.
2. What causes refraction?
Refraction occurs due to differences in optical density between two mediums, causing a change in the speed of light waves.
3. What is Snell's Law?
Snell's Law describes the relationship between the angles of incidence and refraction and the refractive indices of the two mediums involved.
Recent Updates
 Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevati...
 Aman’s salary is first increased by 25% and then decreased by 20%. The result is the ...
 P and S can complete a piece of work in 20 and 15 days respectively. They worked togeth...
 Each day that a library book is kept past its due date, a $0.30 fee is charged at midni...
 Teri goes shopping for some new clothes and then out to lunch with a friend. She spends...
 Two pipes A and B can fill a tank is 8 minutes and 14 minutes respectively. If both the...
 A and B stand at distinct points of a circular race track of length 135 m. They cycle a...
 The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a ...
 In pea plants, Tall plant height is dominant over short plant height. If there are 200 ...
 A wall of length 10 m was to be built across an open ground. The height of the wall is ...
 A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Mr. ...
 In a forest 20% of Mushrooms are Red, 50% Brown and 30% White. A Red mushroom is poison...
 In a large population, 76% of the households own microwaves. A simple random sample of ...
 A bag contains 8 red marbles, 9 yellow marbles, 7 green marbles. How many additional re...
 Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He...