Refraction of Light Class 10th Solutions | Refraction of light SSC Class 10 Questions And Answers
Fill in the blank and Explain the completed sentences.
Refractive index depends on the ______ of light.
Solution 1: Scientific and Written Exam Answer
The refractive index depends on the wavelength of light.
Refractive index (\( n \)) of a medium is given by the formula:
$$ n = \frac{c}{v} $$
where:
- \( c \) = Speed of light in vacuum
- \( v \) = Speed of light in the given medium
The refractive index varies with the wavelength of light because different wavelengths travel at different speeds in a medium. This is why white light disperses into a spectrum when passing through a prism.
Fill in the blank and Explain the completed sentences.
The change in ______ of light rays while going from one medium to another is called refraction.
Solution 1: Scientific and Written Exam Answer
The change in direction of light rays while going from one medium to another is called refraction.
Refraction occurs due to the change in speed of light as it moves between two media with different optical densities. The amount of bending depends on the refractive indices of the two media and is given by Snell’s law:
$$ n_1 \sin \theta_1 = n_2 \sin \theta_2 $$
where:
- \( n_1, n_2 \) = Refractive indices of the two media
- \( \theta_1, \theta_2 \) = Angles of incidence and refraction
Prove the statement:
If the angle of incidence and angle of emergence of a light ray falling on a glass slab are \( i \) and \( e \) respectively, prove that \( i = e \).
Solution 1: Scientific and Written Exam Answer
When a light ray passes through a parallel-sided glass slab, it undergoes two refractions:
- First, at the air-glass interface (incident ray to refracted ray).
- Second, at the glass-air interface (refracted ray to emergent ray).
Let:
- \( i \) = Angle of incidence
- \( r \) = Angle of refraction inside the glass slab
- \( e \) = Angle of emergence
According to Snell’s law at the first interface (air to glass):
$$ n_1 \sin i = n_2 \sin r $$
At the second interface (glass to air):
$$ n_2 \sin r = n_1 \sin e $$
Since the glass slab has parallel sides, the emergent ray is parallel to the incident ray, meaning:
$$ i = e $$
Thus, the angle of incidence is equal to the angle of emergence.
Solution 2: Simple and Understandable Answer
When light enters a glass slab, it bends because its speed changes. But since the slab has parallel sides, the light bends back to its original direction when leaving.
Think of a person entering a swimming pool at an angle and then walking straight across. When they step out, they move in the same direction as before. Similarly, the light ray that enters at an angle \( i \) exits at the same angle \( e \).
So, we can say:
$$ i = e $$
This is why a glass slab does not change the direction of the light permanently—it just shifts the path slightly.
Prove the statement:
A rainbow is the combined effect of refraction, dispersion, and total internal reflection of light.
Solution 1: Scientific and Written Exam Answer
A rainbow is formed due to the interaction of sunlight with raindrops in the atmosphere. The formation of a rainbow involves three main optical phenomena:
- Refraction: When sunlight enters a raindrop, it slows down and bends due to the change in medium from air to water.
- Dispersion: White sunlight is composed of multiple colors, each of which bends at different angles, splitting the light into its spectrum.
- Total Internal Reflection (TIR): The light inside the raindrop is internally reflected off the inner surface before exiting the drop.
After total internal reflection, the light refracts again as it exits the raindrop, further separating into a spectrum of colors. This dispersed light reaches our eyes, forming a rainbow.
Conclusion: The combined effects of refraction, dispersion, and total internal reflection create the beautiful phenomenon of a rainbow.
Solution 2: Simple and Understandable Answer
Imagine a raindrop as a tiny prism in the sky. When sunlight enters the raindrop, three things happen:
- Refraction: The light bends when it enters the drop.
- Dispersion: White light splits into different colors, just like a prism does.
- Total Internal Reflection: The light bounces inside the drop and exits, bending again.
This process occurs in millions of raindrops, and when the light reaches our eyes, we see a colorful rainbow.
Fun Example: Think of how a CD reflects different colors when light shines on it. The colors come from bending and reflecting light—just like a rainbow!
What is the reason for the twinkling of stars?
Options:
- Explosions occurring in stars from time to time
- Absorption of light in the earth’s atmosphere
- Motion of stars
- Changing refractive index of the atmospheric gases ✅
Solution 1: Scientific and Written Exam Answer
Changing refractive index of the atmospheric gases ✅The twinkling of stars is caused by the continuous change in the refractive index of Earth's atmospheric gases. As starlight passes through different layers of the atmosphere, which have varying densities and temperatures, it undergoes refraction multiple times.
Since the atmosphere is always in motion, the direction of the refracted light keeps changing slightly, making the star appear to shift in brightness and position. This phenomenon is called the scintillation or twinkling of stars.
Conclusion: The twinkling of stars is due to the varying refractive index of atmospheric gases, which continuously bends and shifts the path of starlight.
If the refractive index of glass with respect to air is 3/2, what is the refractive index of air with respect to glass?
Options:
- 1/2
- 3
- 2/3 ✅
- 1/3
Solution 1: Scientific and Written Exam Answer
The refractive index of air with respect to glass is the reciprocal of the refractive index of glass with respect to air.
Given:
Refractive index of glass with respect to air: ng/a = 3/2
By the reciprocal formula:
$$ n_{a/g} = \frac{1}{n_{g/a}} $$
Substituting the values:
$$ n_{a/g} = \frac{1}{3/2} = \frac{2}{3} $$
Final Answer: The refractive index of air with respect to glass is 2/3.
Solution 2: Simple and Understandable Answer
The refractive index tells us how much light bends when it moves from one medium to another.
We are given that the refractive index of glass with respect to air is 3/2. To find the refractive index of air with respect to glass, we simply flip the fraction.
Step-by-step:
- Refractive index of glass with respect to air = 3/2
- To find the refractive index of air with respect to glass, take the reciprocal: 2/3
Example: Think of it like speed. If one person is twice as fast as another, then the second person is moving at half the speed in comparison.
Final Answer: The refractive index of air with respect to glass is 2/3.
If in a medium, the speed of light is 1.5 × 108 m/s, how much will the absolute refractive index of that medium be?
Solution:
Understanding Absolute Refractive Index:
The absolute refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (or air) to the speed of light in the given medium.
The formula is:
$$ n = \frac{c}{v} $$
Where:
- n = Absolute refractive index
- c = Speed of light in air/vacuum = 3 × 108 m/s
- v = Speed of light in the given medium = 1.5 × 108 m/s
Calculation:
Substituting the values in the formula:
$$ n = \frac{3 \times 10^8}{1.5 \times 10^8} $$
$$ n = 2 $$
Final Answer:
The absolute refractive index of the medium is 2.
Explanation in Simple Terms:
The refractive index tells us how much light slows down when it enters a medium. In a vacuum (or air), light travels at the highest speed of 3 × 108 m/s. In this medium, it moves at a slower speed of 1.5 × 108 m/s. By dividing these values, we get the refractive index as 2, which means light travels twice as slow in this medium compared to air.
If the absolute refractive indices of glass and water are 3/2 and 4/3 respectively, what is the refractive index of glass with respect to water?
Solution:
Understanding Refractive Index:
The refractive index of one medium with respect to another is given by the formula:
$$ n_{g/w} = \frac{n_g}{n_w} $$
Where:
- ng = Absolute refractive index of glass = 3/2
- nw = Absolute refractive index of water = 4/3
Calculation:
Substituting the given values:
$$ n_{g/w} = \frac{\frac{3}{2}}{\frac{4}{3}} $$
Using division of fractions:
$$ n_{g/w} = \frac{3}{2} \times \frac{3}{4} $$
$$ n_{g/w} = \frac{9}{8} $$
Final Answer:
The refractive index of glass with respect to water is 9/8 or 1.125.
Explanation in Simple Terms:
This means that light slows down slightly when traveling from water to glass. Since the refractive index is greater than 1, it indicates that glass is optically denser than water.