MHT CET · Physics · Ray Optics
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 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
- A \(\sin ^{-1}\left(\frac{1}{\sqrt{\mu}}\right)\)
- B \(\sin ^{-1}\left(\frac{1}{\mu}\right)\)
- C \(\sin ^{-1}\left(\frac{1}{\mu^2}\right)\)
- D \(90^{\circ}\)
Answer & Solution
Correct Answer
(C) \(\sin ^{-1}\left(\frac{1}{\mu^2}\right)\)
Step-by-step Solution
Detailed explanation
In the first case \(\theta\) is the critical angel
Hence, \(\sin \theta=\frac{1}{\mu}\)
In the second case, \(\frac{\sin \theta}{\sin r}=\mu\)
\(
\begin{aligned}
& \therefore \sin r=\frac{\sin \theta}{\mu} \\
& \therefore \sin r=\frac{1}{\mu^2} \\
& \therefore \sin r=\left(\frac{1}{\mu^2}\right)
\end{aligned}
\)
Hence, \(\sin \theta=\frac{1}{\mu}\)
In the second case, \(\frac{\sin \theta}{\sin r}=\mu\)
\(
\begin{aligned}
& \therefore \sin r=\frac{\sin \theta}{\mu} \\
& \therefore \sin r=\frac{1}{\mu^2} \\
& \therefore \sin r=\left(\frac{1}{\mu^2}\right)
\end{aligned}
\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The magnetic moment produced in a sample of 2 gram is \(8 \times 10^{-7} \mathrm{~A} / \mathrm{m}^{2}\). If its density is \(4 \mathrm{~g} / \mathrm{cm}^{3}\), then the magnetization of the sample isMHT CET 2020 Easy
- Two monochromatic beams of intensities I and 4I respectively are superposed to form a steady interference pattern. The maximum and minimum intensities in the pattern areMHT CET 2021 Easy
- The kinetic energy of an electron having de-Broglie wavelength is ( Planck's constant, mass of electron)MHT CET 2018 Medium
- Two waves \(Y_{1}=0 \cdot 25 \sin 316 \mathrm{t}\) and
\(\mathrm{Y}_{2}=0 \cdot 25 \sin 310 \mathrm{t}\)
are propagating along the same direction. The number of beats produced per second areMHT CET 2020 Easy - Alternating current of peak value ampere flows through the primary coil of the transformer. The coefficient of mutual inductance between primary and secondary coil is 1 henry. The peak emf induced in secondary coil is (Frequency of AC = 50 Hz)MHT CET 2016 Easy
- In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential \(V\) and then made to describe semicircular paths of radius \(R\) using a magnetic field \(B\). If \(V\) and \(B\) are kept constant, the ratio \(\left(\frac{\text { charge on the ion }}{\text { mass of the ion }}\right)\) will be proportional toMHT CET 2008 Hard
More PYQs from MHT CET
- The periodic time of a particle doing simple hormonic motion is \(4 \mathrm{~s}\). The time taken by it to go from its mean position to half the maximum displacement (amplitude) isMHT CET 2009 Easy
- The shortest distance between lines \(\bar{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\) and \(\bar{r}=(2 \hat{i}-\hat{j}+2 \hat{k})+\mu(\hat{i}-\hat{j}+\hat{k})\) isMHT CET 2024 Hard
- From point \(P(8,27)\) tangents \(P Q\) and \(P R\) are drawn to the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\). Then, angle subtended by \(Q R\) at origin isMHT CET 2011 Hard
- In an interference experiment, the \(\mathrm{n}^{\text {th }}\) bright fringe for light of wavelength \(\lambda_1(n=0,1,2,3 \ldots)\) coincides with the \(\mathrm{m}^{\text {th }}\) dark fringe for light of wavelength \(\lambda_2(m=1,2,3 \ldots)\). The ratio \(\frac{\lambda_1}{\lambda_2}\) isMHT CET 2024 Easy
- The de-Broglie wavelength \((\lambda)\) of a particle is related to its kinetic energy \((\mathrm{E})\) asMHT CET 2023 Easy
- If the water is being poured at the rate \(36 \mathrm{~m}^3 / \mathrm{sec}\) in cylindrical vessel of base radius \(3 \mathrm{~m}\), then the rate at which water level is rising, isMHT CET 2022 Medium