Total Internal Reflection

Light travels a distance 'x' in time '$t_0$' in air and '$4x$' in time '$t_1$' in another denser medium. The critical angle for this medium is

Consider light travelling from a medium $A$ to medium $B$ separated by a plane interface. If the light undergoes total internal reflection during its travel from medium $A$ to $B$ and the speed of light in media $A$ and $B$ are $2.4 \times 10^{8}\text{ m/s}$ and $2.7 \times 10^{8}\text{ m/s}$, respectively, then the value of critical angle is:

A ray of light is incident at a glass-water interface at an angle $(i_1)$, it emerges finally parallel to the surface of water, then the value of the refractive index of glass $(\mu_g)$ is

$\{\mu_w =$ refractive index of water $= 4/3, \sin(90)^\circ = 1, \cos(90)^\circ = 0\}$

A ray of light takes time '$t$' to travel a distance '$d$' in air and it travels a distance '$4d$', in time '$T$' in a certain medium. If $T = 8t$, the critical angle for the pair of media is

$\left[\sin\left(\frac{\pi}{6}\right) = 0.5, \sin\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}, \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}, \sin\left(\frac{\pi}{2}\right) = 1\right]$

A beam of light is travelling from region I to region IV. The refractive indices in regions I, II, III and IV are $n,\ \frac{n}{2},\ \frac{n}{3}$ and $\frac{n}{4}$ respectively. The angle of incidence for which the beam just misses entering region IV is [$\sin 90^\circ = 1$]

The minimum refractive index of the material of a right-angled isosceles prism as shown in the following figure is

One side of an equilateral prism is painted by a transparent material of refractive index $n_2$. The refractive index of prism is $1.6$. The minimum value of $n_2$ required for total internal reflection from painted face is ________.

A prism of angle $75^\circ$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ______

$(\sin 15^\circ = 0.25$ and $\sin 25^\circ = 0.43)$

The phenomenon, which is not due to total internal reflection is

At the interface between two materials having refractive indices $n_1$ and $n_2$, the critical angle for reflection of an em wave is $\theta_{1C}$. The $n_2$ material is replaced by another material having refractive index $n_3$ such that the critical angle at the interface between $n_1$ and $n_3$ materials is $\theta_{2C}$. If $n_3 > n_2 > n_1; \frac{n_2}{n_3} = \frac{2}{5}$ and $\sin\theta_{2C} - \sin\theta_{1C} = \frac{1}{2}$, then $\theta_{1C}$ is:

A transparent block A having refractive index $\mu = 1.25$ is surrounded by another medium of refractive index $\mu = 1.0$ as shown in the figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in the figure. What is the maximum value of $\theta$ for which light suffers total internal reflection at the top surface of the block?

For a ray of light, the critical angle is minimum, when it travels from

Critical angle of light passing from glass to air is minimum for wavelength of

For a light ray to undergo total internal reflection ( $i =$ angle of incidence, $i_c =$ critical angle)

Critical angle of incidence for a pair of optical media is $45^\circ$. The refractive indices of first and second media are in the ratio:

Velocity of light in diamond is $\left(\frac{5}{12}\right)$th times that in air. Velocity of light in water is $\left(\frac{3}{4}\right)$th times that in air. The angle of incidence of ray of light travelling from water to diamond is (angle of refraction $(r) = 30^\circ) [$ Given $\rightarrow \sin 30^\circ = \frac{1}{2}]$

White light is incident on the interface of glass and air as shown in figure. If green light is just totally internally reflected, then reflected rays inside the glass contain

A light ray is incident on a glass slab of thickness $4\sqrt{3}\text{ cm}$ and refractive index $\sqrt{2}$ The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ $\text{cm}$.

(Given $\sin 15^\circ = 0.25$)

One of the necessary condition for total internal reflection to take place is

( $i =$ angle of incidence, $i_c =$ critical angle)

Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is the critical angle for this medium?

The critical angle for a denser-rarer interface is $45^\circ$. The speed of light in rarer medium is $3 \times 10^{8}\text{ m/s}$. The speed of light in the denser medium is:

A ray of light is incident from air on a glass plate having thickness $\sqrt{3}$ cm and refractive index $\sqrt{2}$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____________ $\times$ 10 $-2$ cm. (given $\sin 15^\circ = 0.26$)

The speed of light in two media $M_1$ and $M_2$ are $1.5 \times 10^{8}\text{ m/s}$ and $2 \times 10^{8}\text{ m/s}$ respectively. If the light undergoes total internal reflection, the critical angle between the two media is

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1.5 $\times$ 108 m/s and 2.0 $\times$ 108 m/s, respectively. The critical angle for a ray of light for these two media is

Light travels in two media $M_1$ and $M_2$ with speeds $1.5 \times 10^{8}\text{ ms}^{-1}$ and $2.0 \times 10^{8}\text{ ms}^{-1}$ respectively. The critical angle between them is:

The speed of light in media 'A' and 'B' are $2.0 \times 10^{10}$ cm/s and $1.5 \times 10^{10}$ cm/s respectively. A ray of light enters from the medium B to A at an incident angle '$\theta$'. If the ray suffers total internal reflection, then

A light wave travelling linearly in a medium of dielectric constant 4, is incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:

(Given: relative permeability of medium $\mu$r = 1)

A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7}$ m. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is x$\pi$ m2. The value of x is __________.

The critical angle for light going from medium '$x$' to medium '$Y$' is $\theta$. The speed of light in medium '$x$' is '$V_x$'. The speed of light in medium '$Y$' is

The critical angle for light going from medium A into medium B is $\theta$. The speed of light in the medium A is $V_A$. What is the speed of light in the medium $B$?

The refractive index of glass is 1.5 and that of water is 1.33. The critical angle for a ray of light going from glass to water is

A ray of light entering from air into a denser medium of refractive index $\frac{4}{3}$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to:

A ray of laser of a wavelength 630 nm is incident at an angle of 30${}^\circ$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2.42 and that of air is 1. Choose the correct option.

A glass slab has refractive index '$\mu$' with respect to air and the critical angle for a ray of light in going from glass to glass to air is '$\theta$' If a ray of light is incident from air on the glass with angle of incidence '$\theta$', then the corresponding angle of refraction is

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure.

The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is:

If the critical angle for total internal reflection from a medium to vacuum is $45^\circ$, then velocity of light in the medium is,

A ray of light travelling through glass of refractive index $\sqrt{2}$ is incident on glass-air boundary at an angle of incidence $45^\circ$. If refractive index of air is 1, then the angle of refraction will be $\left[\sin 45^\circ = \frac{1}{\sqrt{2}}, \sin 90^\circ = 1\right]$

The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability $\frac{4}{3}$ for this wavelength, will be:

There is a small source of light at some depth below the surface of water (refractive index = $\frac{4}{3}$) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly): [Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2$\pi$rh]:

A light ray enters a solid glass sphere of refractive index $\mu = \sqrt{3}$ at an angle of incidence 60°. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is ________.

The critical angle for light going from medium ' $x'$ to medium ' $y$ ' is ' $\theta$ '. The speed of light in medium ' $x$ ' is ' $v_x$ '. The speed of light in medium ' $y$ ' is

In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction?

Glass has refractive index $\mu$ with respect to air and the critical angle for a ray of light going from glass to air is $\theta$. If a ray of light is incident from air on the glass with angle of incidence $\theta$, corresponding angle of refraction is

A transparent cube of side, made of a material of refractive index $\mu$2, is immersed in a liquid of refractive index $\mu_1 (\mu$1 < $\mu$2). A ray is incident on the face AB at an angle $\theta$(shown in the figure). Total internal reflection takes place at point E on the face BC.

Then $\theta$ must satisfy:

In figure, the optical fiber is $l$ = 2m long and has a diameter of d = 20 μm. If a ray of light is incident on one end of the fiber at angle $\theta_1$ = 40°, the number of reflection it makes before emerging from the other end is close to: (refractive index of fibre is 1.31 and sin 40° = 0.64)

Let the refractive index of a denser medium with respect to a rarer medium be n12 and its critical angle be θC. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A is given by:

A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index 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 green light is incident from the water to the air - water interface at the critical angle $(\theta)$. Select the correct statement.

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$ and the diver's eyes are 15 cm below the surface of water. Then the radius of the circle is:

Light is incident from a medium into air at two possible angles of incidence (A) 20° and (B) 40°. In the medium light travels 3.0 cm in 0.2 ns. The ray will:

A light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to:

Which of the following is not due to total internal reflection?

The speed of light in media M1 and M2 are 1.5 $\times$ 108 m/s and 2.0 $\times$ 108 m/s respectively. A ray of light enters from medium M1 to M2 at an incidence angle i. If the ray suffers total internal reflection, the value of i is

A ray of light travelling in a transparent medium of refractive index $\mu$, falls on a surface separating the medium from air at an angle of incidence of 45°. For which of the following value of $\mu$ the ray can undergo total internal reflection?

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}.$ It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.

The incident angle $\theta$ for which the light ray grazes along the wall of the rod is:

A small coin is resting on the bottom of a beaker filled with liquid. A ray of light from the coin travels upto the surface of the liquid and moves along its surface. How fast is the light travelling in the liquid?

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12\text{ cm}$ below the surface, the radius of this circle in $\text{cm}$ is

A light ray is incident perpendicularly to one face of a $90^\circ$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^\circ$, we conclude that the refractive index $n$

Which of the following is used in optical fibres?

For the given incident ray as shown in figure, the condition of total internal reflection of this ray the required refractive index of prism will be

Optical fibre are based on

A disc is placed on a surface of pond which has refractive index 5/3. A source of light is placed 4 m below the surface of liquid. The minimum radius of disc needed so that light is not coming out is,

Light enters at an angle of incidence in a transparent rod of refractive index $n$. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?

A small source of light is 4 m below the surface of water of refractive index 5/3. In order to cut off all the light, coming out of water surface, minimum diameter of the disc placed on the surface of water is