Refraction and Total Internal Reflection

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JEE Main 2021

LEVELJEE Main

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ........... mm. [Take, refractive index of air $= 1.0003$ , wavelength of yellow light in vacuum $= 6000 \overset{˚}{A}$ ]

JEE Advanced 2015

LEVELJEE Advanced

An observer can see through a small hole on the side of a jar (radius $15 cm$ ) at a point at height of $15 cm$ from the bottom (see figure). The hole is at a height of $45 cm$ . When the jar is filled with a liquid up to a height of $30 cm$ , the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is $N /100$ , where $N$ is an integer, the value of $N$ is .......... .

JEE Advanced 1996

LEVELJEE Advanced

A right angled prism ( $4 5^{\circ}$ - $9 0^{\circ}$ - $4 5^{\circ}$ ) of refractive index $n$ has a plane of refractive index $n_{1}$ ( $n_{1} < n$ ) cemented to its diagonal face. The assembly is in air. The ray is incident on $A B$ . (a) Calculate the angle of incidence at $A B$ for which the ray strikes the diagonal face at the critical angle. (b) Assuming $n = 1.352$ , calculate the angle of incidence at $A B$ for which the refracted ray passes through the diagonal face undeviated.

JEE Main 2016

LEVELJEE Main

A transparent slab of thickness $d$ has a refractive index $n (z)$ that increases with $z$ . Here, $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_{1}$ and $n_{2} (> n_{1})$ , as shown in the figure. A ray of light is incident with angle $θ_{i}$ from medium 1 and emerges in medium 2 with refraction angle $θ_{f}$ with a lateral displacement $l$ .

* Multiple Correct Options

(A)

l

is dependent on

n (z)

(B)

n_{1} sin θ_{i} = (n_{2} - n_{1}) sin θ_{f}

(C)

n_{1} sin θ_{i} = n_{2} sin θ_{f}

(D)

l

is independent of

n_{2}

JEE Main 2010

LEVELJEE Main

A large glass slab $(μ = \frac{5}{3})$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R$ cm. What is the value of $R$ ?

JEE Advanced 2014

LEVELJEE Advanced

A point source $S$ is placed at the bottom of a transparent block of height $10 mm$ and refractive index $2.72$ . It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter $11.54 mm$ on the top of the block. The refractive index of the liquid is

Light is incident at an angle $α$ on one planar end of a transparent cylindrical rod of refractive index $n$ . Determine the least value of $n$ so that the light entering the rod does not emerge from the curved surface of the rod irrespective of the value of $α$ .

JEE Advanced 2001

LEVELJEE Main

A ray of light passes through four transparent media with refractive indices $μ_{1}$ , $μ_{2}$ , $μ_{3}$ and $μ_{4}$ as shown in the figure. The surfaces of all media are parallel. If the emergent ray $C D$ is parallel to the incident ray $A B$ , we must have

(A)

μ_{1} = μ_{2}

(B)

μ_{2} = μ_{3}

(C)

μ_{3} = μ_{4}

(D)

μ_{4} = μ_{1}

JEE Main 2003

LEVELJEE Main

A ray of light is incident at the glass-water interface at an angle $i$ , it emerges finally parallel to the surface of water, then the value of $μ_{g}$ would be

(A)

(4/3) sin i

(B)

1/ (sin i)

(C)

4/3

(D)

1

LEVELJEE Main

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence $4 5^{\circ}$ . The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air, select the possible value (s) of $n$ from the following

* Multiple Correct Options

Comprehension Passage

Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index

n_{1}

surrounded by a medium of lower refractive index

n_{2}

. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media

n_{1}

and

n_{2}

as shown in the figure. All rays with the angle of incidence

i

less than a particular value

i_{m}

are confined in the medium of refractive index

n_{1}

. The numerical aperture (NA) of the structure is defined as

sin i_{m}

Question 1:

For two structures namely $S_{1}$ with $n_{1} = \frac{45}{4}$ and $n_{2} = \frac{3}{2}$ , and $S_{2}$ with $n_{1} = \frac{8}{5}$ and $n_{2} = \frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that to air to be 1, the correct options is/are

* Multiple Correct Options

(A)

NA of

S_{1}

immersed in water is the same as that of

S_{2}

immersed in a liquid of refractive index

\frac{16}{3 15}

(B)

NA of

S_{1}

immersed in liquid of refractive index

\frac{6}{15}

is the same as that of

S_{2}

immersed in water

(C)

NA of

S_{1}

placed in air is the same as that

S_{2}

immersed in liquid of refractive index

\frac{4}{15}

(D)

NA of

S_{1}

placed in air is the same as that of

S_{2}

placed in water

Question 2:

If two structures of same cross-sectional area, but different numerical apertures $N A_{1}$ and $N A_{2} (N A_{2} < N A_{1})$ are joined longitudinally, the numerical aperture of the combined structure is

* Multiple Correct Options

(A)

\frac{N A _{1} N A _{2}}{N A _{1} + N A _{2}}

(B)

N A_{1} + N A_{2}

(C)

N A_{1}

(D)

N A_{2}

LEVELJEE Main

A ray of light travelling in water is incident on its surface open to air. The angle of incidence is $θ$ , which is less than the critical angle. Then there will be

(A)

only a reflected ray and no refracted ray

(B)

only a refracted ray and no reflected ray

(C)

a reflected ray and a refracted ray and the angle between them would be less than

18 0^{\circ} - 2 θ

(D)

a reflected ray and a refracted ray and the angle between them would be greater than

18 0^{\circ} - 2 θ

JEE Advanced 1985

LEVELJEE Main

A monochromatic beam of light of wavelength $6000 \overset{˚}{A}$ in vacuum enters a medium of refractive index $1.5$ . In the medium its wavelength is ......, and its frequency is ......

JEE Advanced 2008

LEVELJEE Advanced

A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are $n_{0}$ , $\frac{n _{0}}{2}$ , $\frac{n _{0}}{6}$ and $\frac{n _{0}}{8}$ , respectively. The angle of incidence $θ$ for which the beam just misses entering Region IV is

(A)

sin^{- 1} (\frac{3}{4})

(B)

sin^{- 1} (\frac{1}{8})

(C)

sin^{- 1} (\frac{1}{4})

(D)

sin^{- 1} (\frac{1}{3})

JEE Advanced 2009

LEVELJEE Main

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as

(A)

9 ms^{- 1}

(B)

12 ms^{- 1}

(C)

16 ms^{- 1}

(D)

21.33 ms^{- 1}

JEE Main 2011

LEVELJEE Main

A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence $θ$ . The reflected ( $R$ ) and transmitted ( $T$ ) intensities, both as function of $θ$ , are plotted. The correct sketch is

A right angled prism of refractive index $μ_{1}$ is placed in a rectangular block of refractive index $μ_{2}$ , which is surrounded by a medium of refractive index $μ_{3}$ , as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between $μ_{1}, μ_{2}$ and $μ_{3}$ , it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'. Match the paths in Column I with conditions of refractive indices in Column II and select the correct answer using the codes given below the lists. \begin{array}{ll} \textbf{Column I} & \textbf{Column II} \\ \text{P. } e \rightarrow f & \text{1. } \mu_1 > \sqrt{2}\mu_2 \\ \text{Q. } e \rightarrow g & \text{2. } \mu_2 > \mu_1 \text{ and } \mu_2 > \mu_3 \\ \text{R. } e \rightarrow h & \text{3. } \mu_1 = \mu_2 \\ \text{S. } e \rightarrow i & \text{4. } \mu_2 < \mu_1 < \sqrt{2}\mu_2 \text{ and } \mu_2 > \mu_3 \end{array}

Comprehension Passage

Most materials have the refractive index,

n > 1

. So, when a light ray from air enters a naturally occurring material, then by Snell's law,

\frac{s i n θ _{1}}{s i n θ _{2}} = \frac{n _{2}}{n _{1}}

, it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation,

n = (\frac{c}{v}) = \pm ϵ_{r} μ_{r}

, where

c

is the speed of electromagnetic waves in vacuum,

v

its speed in the medium,

ϵ_{r}

and

μ_{r}

are the relative permittivity and permeability of the medium respectively. In normal materials, both

ϵ_{r}

and

μ_{r}

are positive, implying positive

n

for the medium. When both

ϵ_{r}

and

μ_{r}

are negative, one must choose the negative root of

n

. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behaviour, without violating any physical laws. Since

n

is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.

Question 1:

Choose the correct statement.

(A)

The speed of light in the meta-material is

v = c ∣ n ∣

(B)

The speed of light in the meta-material is

v = \frac{c}{∣ n ∣}

(C)

The speed of light in the meta-material is

v = c

(D)

The wavelength of the light in the meta-material (

λ_{m}

) is given by

λ_{m} = λ_{air} ∣ n ∣

, where

λ_{air}

is the wavelength of the light in air.

Question 2:

For light incident from air on a meta-material, the appropriate ray diagram is

A light wave of frequency $5 \times 1 0^{14} Hz$ enters a medium of refractive index $1.5$ . In the medium the velocity of the light wave is ...... and its wavelength is ......

JEE Advanced 2002

LEVELJEE Advanced

An observer can see through a pin-hole the top end of a thin rod of height $h$ , placed as shown in the figure. The beaker height is $3 h$ and its radius $h$ . When the beaker is filled with a liquid up to a height $2 h$ , he can see the lower end of the rod. Then the refractive index of the liquid is

(A)

\frac{5}{2}

(B)

\frac{5}{2}

(C)

\frac{3}{2}

(D)

\frac{3}{2}

LEVELJEE Main

A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will

(A)

separate the red colour from the green and blue colours

(B)

separate the blue colour from the red and green colours

(C)

separate all the three colours from one another

(D)

not separate even partially any colour from the other two colours.

LEVELJEE Main

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face $A B$ is totally reflected to reach the face $B C$ if

(A)

sin θ > 8/9

(B)

2/3 < sin θ < 8/9

(C)

sin θ < 2/3

A ray of light travelling in air is incident at grazing angle (Incident angle = $9 0^{\circ}$ ) on a long rectangular slab of a transparent medium of thickness $t = 1.0$ m. The point of incidence is the origin $A (0, 0)$ . The medium has a variable index of refraction $n (y)$ given by $n (y) = [k y^{3/2} + 1]^{1/2}$ where $k = 1.0 (m)^{- 3/2}$ . The refractive index of air is 1.0. (1995) (a) Obtain a relation between the slope of the trajectory of the ray at a point $B (x, y)$ in the medium and the incident angle at that point. (b) Obtain an equation for the trajectory $y (x)$ of the ray in the medium. (c) Determine the coordinates $(x_{1}, y_{1})$ of the point $P$ , where the ray intersects the upper surface of the slab-air boundary. (d) Indicate the path of the ray subsequently.

JEE Advanced 1987

LEVELJEE Advanced

A right angled prism is to be made by selecting a proper material and the angles $A$ and $B$ ( $B \leq A$ ), as shown in figure. It is desired that a ray of light incident on the face $A B$ emerges parallel to the incident direction after two internal reflections. (a) What should be the minimum refractive index $μ$ for this to be possible? (b) For $μ = \frac{5}{3}$ is it possible to achieve this with the angle $B$ equal to $3 0^{\circ}$ ?

JEE Advanced 1999

LEVELJEE Advanced

The $x$ - $y$ plane is the boundary between two transparent media. Medium-1 with $z \geq 0$ has a refractive index $2$ and medium-2 with $z \leq 0$ has a refractive index $3$ . A ray of light in medium-1 given by vector $A = 63 \hat{i} + 83 \hat{j} - 10 \hat{k}$ is incident on the plane of separation. Find the unit vector in the direction of the refracted ray in medium-2.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ray of light is incident at the glass-water interface at an angle i, it emerges finally parallel to the surface of water, then the value of μg​ would be

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ray of light travelling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A monochromatic beam of light of wavelength 6000 A˚ in vacuum enters a medium of refractive index 1.5. In the medium its wavelength is ......, and its frequency is ......

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as

Comprehension Passage

Choose the correct statement.

For light incident from air on a meta-material, the appropriate ray diagram is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A light wave of frequency 5×1014 Hz enters a medium of refractive index 1.5. In the medium the velocity of the light wave is ...... and its wavelength is ......

A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. The prism will

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach the face BC if

A ray of light is incident at the glass-water interface at an angle $i$ , it emerges finally parallel to the surface of water, then the value of $μ_{g}$ would be

A ray of light travelling in water is incident on its surface open to air. The angle of incidence is $θ$ , which is less than the critical angle. Then there will be

A monochromatic beam of light of wavelength $6000 \overset{˚}{A}$ in vacuum enters a medium of refractive index $1.5$ . In the medium its wavelength is ......, and its frequency is ......

A light wave of frequency $5 \times 1 0^{14} Hz$ enters a medium of refractive index $1.5$ . In the medium the velocity of the light wave is ...... and its wavelength is ......

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face $A B$ is totally reflected to reach the face $B C$ if