JEE Mains · Physics · STD 12 - Ray optics and optical instruments
- JEE Mains 2022
- Hard
- MCQ
Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of \(\mu_{A}\) to \(\mu_{B}\) is \(1: 2\). Then the thickness of material, in meter is: (Given \(v_{A}\) and \(v_{B}\) are velocities of light in \(A\) and \(B\) materials respectively).
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(5 \times 10^{-10}\,v _{ a } m\)
Step-by-step Solution
Detailed explanation
\(\frac{\mu_{ A }}{\mu_{ B }}=\frac{ c / V _{ A }}{ c / V _{ B }}=\frac{ V _{ B }}{ V _{ A }}=\frac{1}{2}\)
Let the thickness is \(d\)
\(\frac{d}{v_{B}}-\frac{d}{v_{A}}=5 \times 10^{-10}\)
\(d =\frac{5 \times 10^{-10} \times v _{ A } v _{ B }}{ v _{ A }- v _{ B }}\)
As \(v _{ A }=2 v _{ B } \Rightarrow d =5 \times 10^{-10} \times 2 v _{ B }\)
Or \(d =5 \times 10^{-10} \times v_{ A }\)
More questions from Physics
- If \(\overrightarrow{\mathrm{L}}\) and \(\overrightarrow{\mathrm{P}}\) represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector \(\overrightarrow{\mathrm{r}}=\mathrm{a}(\hat{\mathrm{i}} \cos \omega \mathrm{t}+\hat{\mathrm{j}} \sin \omega \mathrm{t})\). The direction of force isJEE Mains 2025 Easy
- Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are
JEE Mains 2019 Hard - Select the correct statement from the followingJEE Mains 2013 Easy
- The work functions of Aluminium and Gold are \(4.1\,eV\) and \(5.1\,eV\) respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is \(.......\)JEE Mains 2023 Medium
- Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For a central force field the angular momentum is a constant.
In the light of the above statements, choose the most appropriate answer from the options given below :JEE Mains 2025 Easy - In a Young’s double slit experiment with slit separation \(0.1\, mm\), one observes a bright fringe at angle \(\frac{1}{{40}}\, rad\) by using light of wavelength \({\lambda _1}\). When the light of wavelength \(\lambda _2\) is used a bright fringe is seen at the same angle in the same set up. Given that \({\lambda _1}\) and \({\lambda _2}\) are in visible range (\(380\, nm\) to \(740\, nm\)), their values areJEE Mains 2019 Medium
More PYQs from JEE Mains
- A person has been using spectacles of power- \(1.0\) diopter for distant vision and a separate reading glass of power \(2.0\) diopters. What is the least distance of distinct vision for this person \(.......cm\)JEE Mains 2023 Hard
- A scooter accelerates from rest for time \(t_{1}\) at constant rate \(a _{1}\) and then retards at constant rate \(a _{2}\) for time \(t _{2}\) and comes to rest. The correct value of \(\frac{t_{1}}{t_{2}}\) will be ..... .JEE Mains 2021 Hard
- Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\)JEE Mains 2022 Medium
- The minimum frequency of photon required to break a particle of mass 15.348 amu into 4\( \alpha \) particles is __________ kHz.
[mass of He nucleus = 4.002 amu,
\(1 amu =1.66 \times 10^{-27} kg, h =6.6 \times 10^{-34} J . s\) and \(c =\) \(\left.3 \times 10^8 m / s \right]\)JEE Mains 2026 Medium