JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
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
- A \(\theta > {\sin ^{ - 1}}\,\frac{{{\mu _1}}}{{{\mu _2}}}\)
- B \(\theta > {\sin ^{ - 1}}\,\sqrt {\frac{{\mu _2^2}}{{\mu _1^2}} - 1} \)
- C \(\theta < {\sin ^{ - 1}}\,\frac{{{\mu _1}}}{{{\mu _2}}}\)
- D \(\theta < {\sin ^{ - 1}}\,\sqrt {\frac{{\mu _2^2}}{{\mu _1^2}} - 1} \)
Answer & Solution
Correct Answer
(D) \(\theta < {\sin ^{ - 1}}\,\sqrt {\frac{{\mu _2^2}}{{\mu _1^2}} - 1} \)
Step-by-step Solution
Detailed explanation
\(\sin \mathrm{c}=\frac{\mu_{1}}{\mu_{2}}\) \(\mu_{1} \sin \theta=\mu_{2} \sin \left(90^o-\mathrm{C}\right)\) \(\sin \theta=\frac{\mu_{2} \sqrt{1-\frac{\mu_{1}^{2}}{\mu_{2}^{2}}}}{\mu_{1}}\) \(\theta=\sin ^{-1} \sqrt{\frac{\mu_{1}^{2}-\mu_{2}^{2}}{\mu_{1}^{2}}}\) For \(TIR\)…
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
- When two soap bubbles of radii \(a\) and \(b ( b > a )\) coalesce, the radius of curvature of common surface isJEE Mains 2021 Hard
- If \({E}, {L}, {m}\) and \({G}\) denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of \({P}\) in the formula \({P}={EL}^{2} {m}^{-5} {G}^{-2}\) areJEE Mains 2021 Medium
- A small circular loop of wire of radius \(a\) is located at the centre of a much larger circular wire loop of radius \(b\). The two loops are in the same plane. The outer loop of radius \(b\) carries an alternating current \(I = I_0\, cos\, (\omega t)\) . The emf induced in the smaller inner loop is nearlyJEE Mains 2017 Hard
- Two cells of emfs \(1\) V and \(2\) V and internal resistance \(2\,\Omega\) and \(1\,\Omega\), respectively connected in parallel, gave a current of \(1\) A through an external resistance. If the polarity of one cell is reversed, then value of current through the external resistance will be \(\dfrac{\alpha}{5}\) A. The value of \(\alpha\) is __________.JEE Mains 2026 Hard
- The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N , the length of the string is 1.56 m. The original length of the string is _____ m.JEE Mains 2025 Medium
- Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be
JEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(A\) denote the event that a \(6 -\)digit integer formed by \(0,1,2,3,4,5,6\) without repetitions, be divisible by \(3 .\) Then probability of event \(A\) is equal to :JEE Mains 2021 Hard
- Consider the sequence \(a_{1}, a_{2}, a_{3}, \ldots \ldots\) such that\(a _{1}=1, a _{2}=2 \text { and } a _{ n +2}=\frac{2}{ a _{ n +1}}+ a _{ n } \text { for } n =1,2,3, \ldots\) If \(\left(\frac{a_{1}+\frac{1}{a_{2}}}{a_{3}}\right) \cdot\left(\frac{a_{2}+\frac{1}{a_{3}}}{a_{4}}\right) \cdot\left(\frac{a_{3}+\frac{1}{a_{4}}}{a_{5}}\right) \cdots\left(\frac{a_{30}+\frac{1}{a_{31}}}{a_{32}}\right)=2^{\alpha}\left({ }^{61} C _{31}\right) .\) then \(\alpha\) is equal to.JEE Mains 2022 Hard
- Figure shows a rod \({AB}\), which is bent in a \(120^{\circ}\) circular arc of radius \(R\). A charge \((-Q)\) is uniformly distributed over rod \({AB}\). What is the electric field \(\overrightarrow{{E}}\) at the centre of curvature \({O}\) ?
JEE Mains 2021 Hard - A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m . The radius of curvature of the curved surface of the lens is _______.JEE Mains 2025 Hard
- If \(\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }\) and \(\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }\) then, The unit vector in the direction of \(\overrightarrow{ P } \times \overrightarrow{ Q }\) is \(\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})\). The value of \(x\) isJEE Mains 2023 Medium
- The dimension of \(\sqrt{\frac{\mu_0}{\epsilon_0}}\) is equal to that of :
( \(\mu_0=\) Vacuum permeability and \(\epsilon_0=\) Vacuum permittivity)JEE Mains 2025 Medium