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Velocity of light travelling from rarer medium to denser medium decreases by 30%. Find the refractive index of the denser medium with respect to rarer medium ?
- a)1.35
- b)1.5
- c)1.4
- d)1.428
Correct answer is option 'D'. Can you explain this answer?
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Velocity of light travelling from rarer medium to denser medium decrea...
Given:
- Velocity of light from rarer medium to denser medium decreases by 30%.
To find:
- Refractive index of the denser medium with respect to rarer medium.
Formula:
- Refractive index (n) = velocity of light in vacuum (c) / velocity of light in the medium (v)
Explanation:
1. Let the velocity of light in the rarer medium be 'v1' and in the denser medium be 'v2'.
2. According to the question, velocity of light decreases by 30% when it travels from rarer to denser medium.
3. Therefore, v2 = v1 - 0.3v1 = 0.7v1
4. Using the formula of refractive index, we get:
- n = c/v2 = c/(0.7v1)
5. Also, we know that the ratio of velocities of light in two media is equal to the ratio of their refractive indices, i.e.
- n2/n1 = v1/v2
6. Substituting the values of v2 and rearranging, we get:
- n2/n1 = v1/v2 = v1/0.7v1 = 1/0.7
- n2/n1 = 1.428
7. Therefore, the refractive index of the denser medium with respect to rarer medium is 1.428 (option D).
Final answer:
- Refractive index of the denser medium with respect to rarer medium = 1.428
- Velocity of light from rarer medium to denser medium decreases by 30%.
To find:
- Refractive index of the denser medium with respect to rarer medium.
Formula:
- Refractive index (n) = velocity of light in vacuum (c) / velocity of light in the medium (v)
Explanation:
1. Let the velocity of light in the rarer medium be 'v1' and in the denser medium be 'v2'.
2. According to the question, velocity of light decreases by 30% when it travels from rarer to denser medium.
3. Therefore, v2 = v1 - 0.3v1 = 0.7v1
4. Using the formula of refractive index, we get:
- n = c/v2 = c/(0.7v1)
5. Also, we know that the ratio of velocities of light in two media is equal to the ratio of their refractive indices, i.e.
- n2/n1 = v1/v2
6. Substituting the values of v2 and rearranging, we get:
- n2/n1 = v1/v2 = v1/0.7v1 = 1/0.7
- n2/n1 = 1.428
7. Therefore, the refractive index of the denser medium with respect to rarer medium is 1.428 (option D).
Final answer:
- Refractive index of the denser medium with respect to rarer medium = 1.428
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Velocity of light travelling from rarer medium to denser medium decreases by 30%. Find the refractive index of the denser medium with respect to rarer medium ?a)1.35b)1.5c)1.4d)1.428Correct answer is option 'D'. Can you explain this answer?
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