Refraction and Dispersion through Prism

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JEE Advanced 1991

LEVELJEE Advanced

Two parallel beams of light $P$ and $Q$ (separation $d$ ) containing radiations of wavelengths $4000 \overset{˚}{A}$ and $5000 \overset{˚}{A}$ (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure. The refractive index of the prism as a function of wavelength is given by the relation, $μ (λ) = 1.20 + \frac{b}{λ ^{2}}$ where $λ$ is in $\overset{˚}{A}$ and $b$ is positive constant. The value of $b$ is such that the condition for total reflection at the face $A C$ is just satisfied for one wavelength and is not satisfied for the other. (a) Find the value of $b$ . (b) Find the deviation of the beams transmitted through the face $A C$ . (c) A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper and the lower beams immediately after transmission from the face $A C$ , are $4 I$ and $I$ respectively, find the resultant intensity at the focus.

JEE Advanced 2017

LEVELJEE Advanced

For an isosceles prism of angle $A$ and refractive index $μ$ , it is found that the angle of minimum deviation $δ_{m} = A$ . Which of the following options is/are correct?

* Multiple Correct Options

(A)

For the angle of incidence

i_{1} = A

, the ray inside the prism is parallel to the base of the prism

(B)

At minimum deviation, the incident angle

i_{1}

and the refracting angle

r_{1}

at the first refracting surface are related by

r_{1} = (\frac{i _{1}}{2})

(C)

For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is

i_{1} = sin^{- 1} [sin A 4 cos^{2} \frac{A}{2} - 1 - cos A]

(D)

For this prism, the refractive index

μ

and the angle prism

A

are related as

A = \frac{1}{2} cos^{- 1} (\frac{μ}{2})

JEE Advanced 2003

LEVELJEE Advanced

A prism of refracting angle $3 0^{\circ}$ is coated with a thin film of transparent material of refractive index $2.2$ on face $A C$ of the prism. A light of wavelength $6600 \overset{˚}{A}$ is incident on face $A B$ such that angle of incidence is $6 0^{\circ}$ . Find (a) the angle of emergence and (b) the minimum value of thickness of the coated film on the face $A C$ for which the light emerging from the face has maximum intensity. (Given refractive index of the material of the prism is $3$ )

JEE Advanced 1998

LEVELJEE Advanced

A prism of refractive index $n_{1}$ and another prism of refractive index $n_{2}$ are stuck together with a gap as shown in the figure. The angles of the prism are as shown. $n_{1}$ and $n_{2}$ depend on $λ$ , the wavelength of light according to : $n_{1} = 1.20 + \frac{10.8 \times 1 0 ^{4}}{λ ^{2}}$ and $n_{2} = 1.45 + \frac{1.80 \times 1 0 ^{4}}{λ ^{2}}$ where $λ$ is in nm. (a) Calculate the wavelength $λ_{0}$ for which rays incident at any angle on the interface $B C$ pass through without bending at that interface. (b) For light of wavelength $λ_{0}$ , find the angle of incidence $i$ on the face $A C$ such that the deviation produced by the combination of prisms is minimum.

LEVELJEE Main

A given ray of light suffers minimum deviation in an equilateral prism $P$ . Additional prisms $Q$ and $R$ of identical shape and of the same material as $P$ are now added as shown in the figure. The ray will suffer

same deviation as before

(D)

total internal reflection

LEVELJEE Main

A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true ?

Either PQ or RS is horizontal

JEE Main 2008

LEVELJEE Main

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $6 0^{\circ}$ ). In the position of minimum deviation, the angle of refraction will be

(A)

30° for both the colours

(B)

greater for the violet colour

(C)

greater for the red colour

(D)

equal but not 30° for both the colours

JEE Advanced 1992

LEVELJEE Main

A ray of light undergoes deviation of $3 0^{\circ}$ when incident on an equilateral prism of refractive index $2$ . The angle made by the ray inside the prism with the base of the prism is ______

LEVELJEE Main

A thin prism $P_{1}$ with angle $4^{\circ}$ and made from glass of refractive index $1.54$ is combined with another thin prism $P_{2}$ made from glass of refractive index $1.72$ to produce dispersion without deviation. The angle of the prism $P_{2}$ is

(A)

5.3 3^{\circ}

(B)

4^{\circ}

(C)

3^{\circ}

(D)

2. 6^{\circ}

LEVELJEE Main

A ray of light is incident normally on one of the faces of a prism of apex angle $3 0^{\circ}$ and refractive index $2$ . The angle of deviation of the ray is ...... degrees.

JEE Advanced 2001

LEVELJEE Advanced

The refractive indices of the crown glass for blue and red light are 1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle $6^{\circ}$ is made of crown glass. A beam of white light is incident at a small angle on this prism. The other flint glass isosceles prism is combined with the crown glass prism such that there is no deviation of the incident light. (a) Determine the angle of the flint glass prism. (b) Calculate the net dispersion of the combined system.

JEE Advanced 2015

LEVELJEE Advanced

A monochromatic beam of light is incident at $6 0^{\circ}$ on one face of an equilateral prism of refractive index $n$ and emerges from the opposite face making an angle $θ (n)$ with the normal (see figure). For $n = 3$ the value of $θ$ is $6 0^{\circ}$ and $\frac{d θ}{d n} = m$ . The value of $m$ is

JEE Advanced 1978

LEVELJEE Main

A ray of light is incident at an angle of 60° on one face of a prism which has an angle of 30°. The ray emerging out of the prism makes an angle of 30° with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of the lens.

JEE Advanced 2005

LEVELJEE Advanced

A ray of light is incident on a prism $A B C$ of refractive index $3$ as shown in figure. (a) Find the angle of incidence for which the deviation of light ray by the prism $A B C$ is minimum. (b) By what angle the second identical prism must be rotated, so that the final ray suffers net minimum deviation.

LEVELJEE Advanced

An isosceles prism of angle $12 0^{\circ}$ has a refractive index $1.44$ . Two parallel rays of monochromatic light enter the prism parallel to each other in air as shown. The rays emerging from the opposite face

(A)

are parallel to each other

2 [sin^{- 1} (0.72) - 3 0^{\circ}]

with each other

(D)

make an angle

2 sin^{- 1} (0.72)

with each other

JEE Advanced 2024

LEVELJEE Advanced

Two equilateral-triangular prisms $P_{1}$ and $P_{2}$ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism $P_{1}$ at an angle of incidence $θ$ such that the outgoing ray undergoes minimum deviation in prism $P_{2}$ . If the respective refractive indices of $P_{1}$ and $P_{2}$ are $\frac{3}{2}$ and $3$ , then $θ = sin^{- 1} [\frac{3}{2} sin (\frac{π}{β})]$ , where the value of $β$ is

JEE Advanced 2023

LEVELJEE Advanced

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $δ = 6 0^{\circ}$ (see Figure-1). The angle of minimum deviation for red light from the same prism is $δ_{min} = 3 0^{\circ}$ (see Figure-2). The refractive index of the prism material for blue light is $3$ . Which of the following statement(s) is(are) correct?

* Multiple Correct Options

(A)

The blue light is polarized in the plane of incidence.

(B)

The angle of the prism is

4 5^{\circ}

(C)

The refractive index of the material of the prism for red light is

2

(D)

The angle of refraction for blue light in air at the exit plane of the prism is

6 0^{\circ}

JEE Advanced 2026

LEVELJEE Advanced

Consider two isosceles prisms 1 and 2 with prism angles $A_{1}$ and $A_{2}$ and refractive indices $n_{1}$ and $n_{2}$ , respectively, as shown in the figure. The faces $a_{1} b_{1}$ and $a_{2} b_{2}$ are parallel to each other and perpendicular to the mirror $M$ . If a ray of light is incident on the face $a_{1} c_{1}$ and emerges from the face $a_{2} c_{2}$ , then the correct statement(s) is/are:

* Multiple Correct Options

(A)

If both the prisms are at minimum deviation condition, then

\frac{n _{2}}{n _{1}} = sin (\frac{A _{1}}{2}) / sin (\frac{A _{2}}{2})

(B)

If prism 2 is at minimum deviation condition, then

sin i_{1} = n_{2} sin (\frac{A _{2}}{2})

is always true.

(C)

If both the prisms 1 and 2 are thin and are at minimum deviation condition with angles of deviation

δ_{m_{1}}

and

δ_{m_{2}}

, respectively, then

θ = \frac{δ _{m_{1}}}{2 ( n _{1} - 1 )} + \frac{δ _{m_{2}}}{2 ( n _{2} - 1 )}

(D)

If prism 1 is at minimum deviation condition, then

sin i_{2} = n_{1} sin (\frac{A _{1}}{2})

is always true.

JEE Advanced 2026

LEVELJEE Advanced

A beam of polychromatic light passes through a thin prism of prism angle $6^{\circ}$ . The refractive index of the material of the prism varies with wavelength ( $λ$ ) as $n (λ) = α λ + \frac{β}{λ ^{2}}$ , where $α = 3 μ m^{- 1}$ and $β = 0.096 μ m^{2}$ . If $λ_{min}$ is the wavelength at which the angle of minimum deviation $D_{m}$ is smallest, then the correct value of $D_{m}$ at $λ_{min}$ is

(A)

6. 4^{\circ}

(B)

4. 8^{\circ}

(C)

3. 2^{\circ}

(D)

2. 4^{\circ}

JEE Advanced 2021

LEVELJEE Advanced

For a prism of prism angle $θ = 6 0^{\circ}$ , the refractive indices of the left half and the right half are, respectively, $n_{1}$ and $n_{2}$ ( $n_{2} \geq n_{1}$ ) as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays will have minimum deviation if $n_{1} = n_{2} = n = 1.5$ . For the case of unequal refractive indices, $n_{1} = n$ and $n_{2} = n + Δ n$ (where $Δ n ≪ n$ ), the angle of emergence $e = i + Δ e$ . Which of the following statement(s) is (are) correct?

* Multiple Correct Options

(A)

The value of

Δ e

(in radians) is greater than that of

Δ n

(B)

Δ e

is proportional to

Δ n

(C)

Δ e

lies between 2.0 and 3.0 milliradians, if

Δ n = 2.8 \times 1 0^{- 3}

(D)

Δ e

lies between 1.0 and 1.6 milliradians, if

Δ n = 2.8 \times 1 0^{- 3}

JEE Main 2021

LEVELJEE Main

A ray of light passing through a prism ( $μ = 3$ ) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ……… (in degrees).

JEE Main 2016

LEVELJEE Advanced

In an experiment for determination of refractive index of glass of a prism by $i - δ$ , plot, it was found that a ray incident at an angle $3 5^{\circ}$ suffers a deviation of $4 0^{\circ}$ and that it emerges at an angle $7 9^{\circ}$ . In that case, which of the following is closest to the maximum possible value of the refractive index?

Cross-section view of a prism is the equilateral triangle $A B C$ in the figure. The minimum deviation is observed using this prism when the angle of incidence is equal to the prism angle. The time taken by light to travel from $P$ (mid-point of $B C$ ) to $A$ is ..... $\times 1 0^{- 10}$ s. (Given, speed of light in vacuum $= 3 \times 1 0^{8}$ m/s and $cos 3 0^{\circ} = \frac{3}{2}$ )

LEVELJEE Main

The refractive index of glass is $1.520$ for red light and $1.525$ for blue light. Let $D_{1}$ and $D_{2}$ be angles of minimum deviations for red and blue light respectively in a prism of this glass. Then,

(A)

D_{1} < D_{2}

(B)

D_{1} = D_{2}

(C)

can be less than or greater than

D_{2}

depending upon the angle of prism

(D)

D_{1} > D_{2}

JEE Main 2021

LEVELJEE Main

The expected graphical representation of the variation of angle of deviation $δ$ with angle of incidence $i$ in a prism is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation δm​=A. Which of the following options is/are correct?

A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true ?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A ray of light is incident normally on one of the faces of a prism of apex angle 30∘ and refractive index 2​. The angle of deviation of the ray is ...... degrees.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The expected graphical representation of the variation of angle of deviation δ with angle of incidence i in a prism is

For an isosceles prism of angle $A$ and refractive index $μ$ , it is found that the angle of minimum deviation $δ_{m} = A$ . Which of the following options is/are correct?

A ray of light is incident normally on one of the faces of a prism of apex angle $3 0^{\circ}$ and refractive index $2$ . The angle of deviation of the ray is ...... degrees.

The expected graphical representation of the variation of angle of deviation $δ$ with angle of incidence $i$ in a prism is