Two transparent media A and B are separated by a plane boundary. The speed of light in those media are $1.5 \times 10^8 m/s$ and $2.0 \times 10^8 m/s$, respectively. The critical angle for a ray of light for these two media is:
(2022)
Critical angle is given by $\sin \theta_c = \frac{\mu_{rarer}}{\mu_{denser}} = \frac{v_{denser}}{v_{rarer}}$.
The speed of light is lower in the denser medium, so $v_{denser} = 1.5 \times 10^8 m/s$ and $v_{rarer} = 2.0 \times 10^8 m/s$.
$\sin \theta_c = \frac{1.5 \times 10^8}{2.0 \times 10^8} = 0.750$, leading to $\theta_c = \sin^{-1}(0.750)$.
If the critical angle for total internal reflection from a medium to vacuum is $45^\circ$, then velocity of light in the medium is,
(2020-Covid)
For total internal reflection to vacuum, critical angle $\theta_c$ satisfies $\sin \theta_c = \frac{1}{\mu}$.
Given $\theta_c = 45^\circ$, we have $\mu = \frac{1}{\sin(45^\circ)} = \sqrt{2}$.
Velocity of light in the medium is $v = \frac{c}{\mu} = \frac{3}{\sqrt{2}} \times 10^8 m/s$.
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?
(2019)
The critical angle is defined as the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly $90^\circ$.
When the angle of incidence equals the critical angle, the refracted ray grazes the interface.
Therefore, the angle of refraction is $90^\circ$.
A light ray falls on a glass surface of refractive index $\sqrt{3}$, at an angle $60^\circ$. The angle between the refracted and reflected rays would be :
(2022)
By Snell's law, $1 \times \sin(60^\circ) = \sqrt{3} \times \sin(r)$, which gives $\sin(r) = 1/2$, so angle of refraction $r = 30^\circ$.
By law of reflection, angle of reflection is equal to angle of incidence $i = 60^\circ$.
Angle between reflected and refracted rays is $180^\circ - (i + r) = 180^\circ - (60^\circ + 30^\circ) = 90^\circ$.
A thin prism having refracting angle $10^\circ$ is made of glass of refractive index $1.42$. This prism is combined with another thin prism of glass of refractive index $1.7$. This combination produces dispersion without deviation. The refracting angle of second prism should be:
(2017-Delhi)
For dispersion without deviation, the net deviation produced by the combination must be zero.
$(\mu_1 - 1)A_1 = (\mu_2 - 1)A_2$, where A and $\mu$ are refracting angle and refractive index.
$(1.42 - 1) \times 10^\circ = (1.7 - 1) \times A_2$, giving $4.2 = 0.7 A_2$, so $A_2 = 6^\circ$.
A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3 cm$ and refractive index $1.5$ is placed over the mark. How should the microscope be moved to get the mark in focus again?
(2006)
When a glass slab is placed over a mark, the mark appears raised by a distance known as normal shift.
Normal shift $\Delta t = t(1 - \frac{1}{\mu}) = 3(1 - \frac{1}{1.5}) = 3(1 - \frac{2}{3}) = 1 cm$.
To focus again on the apparent image, the microscope must be moved $1 cm$ upward.
A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from:
(2004)
When composite light is incident obliquely on a parallel-sided glass slab, different colors undergo different refraction angles due to dispersion.
They suffer different lateral shifts but emerge parallel to the incident ray direction.
Thus, red and green rays emerge from two points propagating in two different parallel directions.
Light travels through a glass plate of thickness t and having a refractive index $\mu$. If c is the velocity of light in vacuum, the time taken by light to travel this thickness of glass is
(1996)
The velocity of light in the glass medium is $v = \frac{c}{\mu}$.
Time taken to travel thickness t is given by $T = \frac{distance}{velocity} = \frac{t}{v}$.
Substituting the velocity, $T = \frac{t}{c/\mu} = \frac{\mu t}{c}$.
Which of the following is not due to total internal reflection?
(2011 Pre)
The difference between apparent and real depth of a pond is due to refraction of light. Optical fibers, mirages, and the brilliance of diamonds are all phenomena based on total internal reflection.
The speed of light in media $M_1$ and $M_2$ is $1.5 \times 10^8 m/s$ and $2.0 \times 10^8 m/s$ respectively. A ray of light enters from medium $M_1$ to $M_2$ at an incidence angle $i$. If the ray suffers total internal reflection, the value of $i$ is:
(2010 Mains)
Critical angle is $\sin \theta_c = \frac{\mu_2}{\mu_1} = \frac{v_1}{v_2} = \frac{1.5 \times 10^8}{2.0 \times 10^8} = \frac{3}{4}$. For total internal reflection, the angle of incidence must be greater than or equal to the critical angle, so $i \ge \sin^{-1}\left(\frac{3}{4}\right)$.