Critical Angle and Total Internal Reflection PYQs: JEE Mains Physics

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1. 1. 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 ___________ .
   \(\left(\sin 15^{\circ}=0.25\right.\) and \(\left.\sin 25^{\circ}=0.43\right)\) 2026 Easy
2. 2. 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 \(2.4 \times 10^8 m / s\) and \(2.7 \times 10^8 m / s\) respectively, then the value of critical angle is : 2026 Hard
3. 3. A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is _______.
   2025 Hard
4. 4. A transparent block A having refractive index \(\mu=1.25\) is surrounded by another medium of refractive index \(\mu=1.0\) as shown in figure. A light ray is incident on the flat face of the block with incident angle \(\theta\) as shown in figure. What is the maximum value of \(\theta\) for which light suffers total internal reflection at the top surface of the block?
   2025 Medium
5. 5. At the interface between two materials having refractive indices \(n_1\) and \(n_2\), the critical angle for reflection of an em wave is \(\theta_{1 C}\). 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 \(\theta_{2 \mathrm{C}}\). If \(\mathrm{n}_3\gt\mathrm{n}_2\gt\mathrm{n}_1 ; \frac{\mathrm{n}_2}{\mathrm{n}_3}=\frac{2}{5}\) and \(\sin \theta_{2 \mathrm{C}}-\sin \theta_{1 \mathrm{C}}=\frac{1}{2}\), then \(\theta_{1 \mathrm{C}}\) is : 2025 Hard
6. 6. 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 _______. 2024 Hard
7. 7. 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 \(.......\times 10^{-2}\) (given \(\sin 15^{\circ}=0.26\) ) 2023 Medium
8. 8. The critical angle for a denser-rarer interface is \(45^{\circ}\). The speed of light in rarer medium is \(3 \times 10^8\) ms. The speed of light in the denser medium is: 2023 Medium
9. 9. A light wave travelling linearly in a medium of dielectric constant \(4,\) 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 \(\mu_{ s }=1)\)  2022 Hard
10. 10. 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 \(x \,\pi m ^{2}\). The value of \(x\) is ............... 2022 Medium
11. 11. Light travels in two media \(M _{1}\) and \(M _{2}\) with speeds \(1.5 \times 10^{8} ms ^{-1}\) and \(2.0 \times 10^{8} ms ^{-1}\) respectively. The critical angle between them is. 2022 Medium
12. 12. 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 2022 Medium
13. 13. 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 -
    2021 Hard
14. 14. 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.....\(^o\) 2020 Medium
15. 15. A transparent cube of side \(d\), 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 \(BC\). The \(\theta\) must satisfy
    2019 Hard
16. 16. In figure, the optical fiber is \(I = 2\,m\) long and has a diameter of \(d = 20\,\mu \,m\). If a ray of light is incident on one end of the fiber at angle \({\theta _1} = {40^o}\) , the number of reflection it makes before emerging from the other end is close to
    2019 Hard
17. 17. Let the refractive index of a denser medium with respect to a rarer medium be \(n_{12}\) and its critical angle be \(\theta_C\).  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 \(90^o\).  Angle \(A\) is given by 2017 Hard
18. 18. 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 2014 Hard
19. 19. A green light is incident from the water to the air - water interface at the critical angle \((\theta)\). Select the correct statement . 2014 Easy
20. 20. Light is incident from a medium into air at two possible angles of incidence \((A)\, 20^o\) and \((B)\, 40^o\) . In the medium light travels \(3.0\, cm\) in \(0.2\, ns\). The ray will 2013 Hard

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