KCET · Physics · Ray Optics
A ray of light passes from vaccum into a medium of refractive index \(n\). If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is
- A \(\operatorname{Sin}^{-1}\left(\frac{n}{2}\right)\)
- B \(2 \operatorname{Cos}^{-1}\left(\frac{n}{2}\right)\)
- C \(2 \operatorname{Sin}^{-1}\left(\frac{\mathrm{n}}{2}\right)\)
- D \(\operatorname{Cos}^{-1}\left(\frac{n}{2}\right)\)
Answer & Solution
Correct Answer
(B) \(2 \operatorname{Cos}^{-1}\left(\frac{n}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & 1 \times \sin i=n \sin \frac{i}{2} \\ & 2 \sin \frac{i}{2} \cos \frac{i}{2}=n \sin \frac{i}{2} \\ & 2 \cos \frac{i}{2}=n \\ & \cos \frac{i}{2}=\frac{n}{2} \\ & \frac{i}{2}=\cos ^{-1}\left(\frac{n}{2}\right) \\ & i=2 \cos ^{-1}\left(\frac{n}{2}\right)\end{aligned}\)
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 energy stored in an inductor of self inductance \(L\) henry carrying a current of \(I\) ampere isKCET 2011 Easy
- A uniform magnetic field of strength \(B=2 \mathrm{mT}\) exists vertically downwards. These magnetic field lines pass through a closed surface as shown in the figure. The closed surface consists of a hemisphere \(S_1\), a right circular cone \(S_2\) and a circular surface \(S_3\). The magnetic flux through \(S_1\) and \(S_2\) are respectively.
KCET 2024 Medium - Moment of Inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \( I \). If the same rod is bent into a ring and its moment of inertia about its diameter is \( I^{\prime} \) then the ratio \( \frac{I}{I^{\prime}} \) isKCET 2015 Easy
- In a system of two crossed polarisers, it is found that the intensity of light from the second
polariser is half from that of first polariser. The angle between their pass axes isKCET 2017 Medium - A mass ' \( m \) ' on the surface of the Earth is shifted to a target equal to the radius of the Earth. If
' \( R \) ' is the radius and ' \( M \) ' is the mass of the Earth, then work done in this process isKCET 2018 Medium - Which of the following statements is false in the case of polar molecules?KCET 2021 Medium
More PYQs from KCET
- Match the organic compounds listed under Column-I with the explanation given under Column-II. Choose the appropriate option from the given choices.
Column-I Column-II A. Phosphoenol pyruvate (PEP) p. 6-carbon compound B. Ribulose biphosphate (RuBP) q. 2-carbon compound C. Oxaloacetic acid (OAA) r. 4-carbon compound D. Acetyl coenzymeA s. 5-carbon compound t. 3-carbon compound KCET 2014 Medium - Maximum acceleration of the train in which a \( 50 \mathrm{~kg} \) box lying on its floor will remain stationary
(Given : Co-efficient of static friction between the box and the train's floor is \( 0.3 \) and
\( g=10 m s^{-2} \) )KCET 2016 Medium - A dipole moment \(p\) and moment of inertia \(I\) is placed in a uniform electric field \(\mathbf{E}\). If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole isKCET 2020 Easy
- The number of moles of hydrogen that can be added to 1 mole of an oil is the highest inKCET 2012 Hard
- If the roots of the equation \(x^{3}+a x^{2}+b x+c=0\) are in \(\mathrm{AP}\), then \(2 a^{3}-9 a b\) is equal toKCET 2013 Medium
- If one mole of ammonia and one mole of hydrogen chloride are mixed in a closed container to form ammonium chloride gas, thenKCET 2008 Easy