JEE Mains · Physics · STD 12 - 10. Wave optics
Consider a tank made of glass (refractive index \(1.5\)) with a thick bottom. It is filled with a liquid of refractive index \(\mu \). A student finds that, irrespective of what the incident angle \(I\) (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of \(\mu \) is
- A \(\sqrt {\frac{5}{3}} \)
- B \(\frac{3}{{\sqrt 5 }}\)
- C \(\frac{5}{{\sqrt 3 }}\)
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{{\sqrt 5 }}\)
Step-by-step Solution
Detailed explanation
\(\sin 90^{\circ}=\mu \sin \theta\) \(\Rightarrow \quad \sin \theta=\frac{1}{\mu}\) \({\mu \sin \theta=1.5 \sin r}\) \({\mu \tan \theta=1.5}\) \( \Rightarrow \tan \theta = \frac{{1.5}}{\mu }\) \(\sin \theta = \frac{3}{{\sqrt {9 + 4{\mu ^2}} }} = \frac{1}{\mu }\)…
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
- Given below are two statements: Statement \(I\) : A uniform wire of resistance \(80\,\Omega\) is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be \(5\,\Omega\). Statement \(II :\) Two resistance \(2\,R\) and \(3\,R\) are connected in parallel in a electric circuit. The value of thermal energy developed in \(3\,R\) and \(2\,R\) will be in the ratio \(3:2.\) In the light of the above statements, choose the most appropriate answer from the options given belowJEE Mains 2022 Medium
- The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )JEE Mains 2026 Easy - Identify the physical quantity that cannot be measured using spherometer :JEE Mains 2024 Hard
- The potential energy of a particle of mass \(4\,kg\) in motion along the \(x\)-axis is given by \(U =4(1-\cos 4 x )\,J\). The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is \(\left(\frac{\pi}{ K }\right)\,s\). The value of \(K\) is .......JEE Mains 2022 Hard
- The magnetic moments associated with two closely wound circular coils \(A\) and \(B\) of radius \(r_A=10 cm\) and \(r_B=20 cm\) respectively are equal if: (Where \(N _A, I _{ A }\) and \(N _B, I _{ B }\) are number of turn and current of \(A\) and \(B\) respectively)JEE Mains 2023 Medium
- A Carnot's engine works as a refrigerator between \(250\, K\) and \(300\, K\). It receives \(500\, cal\) heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is ..... \(J\)JEE Mains 2018 Medium
More PYQs from JEE Mains
- The parabolas : \(a^2+2 b x+c y=0\) and \(d x^2+2 ex + fy =0\) intersect on the line \(y=1\). If \(a, b, c, d, e, f\) are positive real numbers and \(a , b , c\) are in \(G.P.\), thenJEE Mains 2023 Hard
- The coefficient of \(x^{70}\) in \(x^2(1+x)^{98}+x^3(1+x)^{97}+\) \(x^4(1+x)^{96}+\ldots \ldots . .+x^{54}(1+x)^{46}\) is \({ }^{99} \mathrm{C}_p-{ }^{46} \mathrm{C}_{\mathrm{q}}\). Then a possible value to \(\mathrm{p}+\mathrm{q}\) is :JEE Mains 2024 Hard
- Let \(a_1, a_2, \ldots \ldots, a_n\) be in A.P. If \(a_5=2 a_7\) and \(a_{11}=18\), then \(12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots . \cdot \frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)\) is equal to \(..........\).JEE Mains 2023 Hard
- If the following system of linear equations \(2 x+y+z=5\) \(x-y+z=3\) \(x+y+a z=b\) has no solution, then :JEE Mains 2021 Hard
- Let \(y=x\) be the equation of a chord of the circle \(C_{1}\) (in the closed half-plane \(x\ge0)\) of diameter 10 passing through the origin. Let \(C_{2}\) be another circle described on the given chord as its diameter. If the equation of the chord of the circle \(C_{2}\), which passes through the point (2, 3) and is farthest from the center of \(C_{2}\), is \(x+ay+b=0,\) then \(a-b\) is equal to:JEE Mains 2026 Easy
- If the screw on a screw-gauge is given six rotations, it moves by \(3\; \mathrm{mm}\) on the main scale. If there are \(50\) divisions on the circular scale the least count of the screw gauge isJEE Mains 2020 Medium