Refraction of light 10th class (lec-5)

 video lecture for Refraction of light 

Question 1. The refractive indices of glass and water with respect to air are `3/2` and `4/3` respectively. If speed of light in glass is `2\times10^{8} ms^{-1}`, find the speed of light in water. (AI 2016)

Question 2. The absolute refractive indices of glass and water are `4/3` and `3/2` respectively. If the speed of light in glass is `2\times10^{8} ms^{-1}`, calculate the speed of light in (i) vacuum, (ii) water. (AI 2015)

Question 3. “A ray of light incident on a rectangular glass slab immersed in any medium emerges parallel to itself.” Draw labelled ray diagram to justify the statement”. (Delhi 2013)

Question 4: The absolute refractive indices of glass and water are `1.5` and `1.33` respectively. In which medium does light travel faster? Calculate the ratio of speeds of light in the two media. (Delhi 2013 C)

Question 5. (a) Water has refractive index `1.33` and alcohol has refractive index `1.36`. Which of the two medium is optically denser? Give reason for your answer. (b) Draw a ray diagram to show the path of a ray of light passing obliquely from water to alcohol. (c) State the relationship between angle of incidence and angle of refraction in the above case. (2020)

Question 6. The refractive index of a medium `V` with respect to a medium `‘y’` is `2/3` and the refractive index of medium `‘y’` with respect to medium `‘z’` is `4/3`. Find the refractive index of medium `z` with respect to medium `V``.

If the speed of light in medium `‘x’` is `3\times10^{8} ms^{-1}`, calculate the speed of light in medium `‘y’`. (2020)

Question 7. If the refractive index of glass for light going from air to glass is `3/2`, find the refractive index of air for light going from glass to air. (Delhi 2016)

Question 8. What is the principle of reversibility of light? Show that the incident of light is parallel to the emergent ray of light when light falls obliquely on a side of a rectangular glass slab. (AI 2011)

Answer key

Q1: Answer:

Q2: Answer:

Given that: `n_{g} = 4/3, n_{w} = 3/2, v_{g} = 2\times10^{8} ms^{-1}`

Absolute refractive index of a medium, `n_{m}=\frac{c}{v}`

where, `c` is the speed of light in vacuum and v is the speed of light in medium.

Note: The values given in question are not correct as the speed of light in vacuum is 

`3\times10^{8} ms^{-1}`

Q3: Answer

Q4: Answer:

Given : refractive index of glass, `n_{g} = 1.5`

Refractive index of water, `n_{w} = 1.33`

Since, refractive index of medium,

For glass `n_{g}=\frac{c}{v_{g}}` ……… (i)

For water `n_{w}=\frac{c}{v_{w}}`……… (ii)

Since velocity of light in medium is inversely proportional to its refractive index, the light will travel faster in optically rarer medium i.e., water.

Dividing (i) by (ii),

So, the ratio of `v_{g}` and `v_{w}` is `1.33 : 1.5.`

Q5: Answer:

(a) Here, alcohol is optically denser medium as its refractive index is higher than that of water. When we compare the two media, the one with larger refractive index is called the optically denser medium than the other as the speed of light is lower in this medium. (b) Since light is travelling from water (rarer medium) to alcohol (denser medium), it slows down and bends towards the normal..

where i = angle of incidence and r = angle of refraction.

(c) According to Snell’s law,

`\frac{sin i}{sin r}=\frac{μalcohol}{μwater}=\frac{1.36}{1.33}=1.0225`

`∴ sin i = 1.0225\timessin r`

Q6: Answer:

Given, refractive index of medium x with respect to `y`, `y_{µX} = 2/3` Refractive index of medium y with respect to `z`, `Z_{µY} = 4/3` ∴ Refractive index of medium x with respect to `z`, `Z_{µX} = Y_{µX} . Z_{µY} = 2/3\times4/3 = 8/9` ∴ Refractive index of medium z with respect to x, `X_{µY} = \frac{1}{Z_{µX}} = 9/8` Now speed of light in `x = 3\times10^{8} ms^{-1}` Speed of light in `y`, `v_{Y} = ?`

`⇒ v_{Y}= 2/3\times3\times10^{8}=2\times10^{8} ms^{-1}`

Q7: Answer:

Refractive index of glass w.r.t air is `3`

`gn_{a} = 3/2`

Now, refractive index of air w.r.t glass will be

`an_{g}= \frac{1}{gn_{a}} = 1/(3/2) = 2/3`

Q8: Answer:

Principle of reversibility of light states that the light will follow exactly the same path if the direction is reversed.

Using Snell’s law of refraction, `\frac{sin i}{sin r_{1}}=\frac{sin e}{sin r_{2}}`

Since `r_{1}=r_{2}, so i = e`

so `PQ` is parallel to `RS`.

So, we conclude that incident ray is parallel to the emergent ray.