JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm . Refractive index of glass is 1.5 . The rays converge to a point at a distance x cm from the centre of the curvature of the spherical surface. The value of x is __________ cm.
- A 50
- B 100
- C 150
- D 200
Answer & Solution
Correct Answer
(B) 100
Step-by-step Solution
Detailed explanation
\( \frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}\Rightarrow\frac{1.5}{v}-\frac{1}{\infty}=\frac{1.5-1}{50} \) \( V=150~cm \) \(x \rightarrow\) measure from center x = V - R = 150 - 50 = 100 cm
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
- An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass \(M\). The piston and the cylinder have equal cross sectional area \(A\). When the piston is in equilibrium, the volume of the gas is \(V_0\) and its pressure is \(P_ 0\). The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequencyJEE Mains 2013 Hard
- A circular disc \(D_1\) of mass \(M\) and radius \(R\) has two identical discs \(D_2\) and \(D_3\) of the same mass \(M\) and radius \(R\) attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis \(OO\)’, passing through the centre of \(D_1\) as shown in the figure, will
JEE Mains 2019 Hard - \(27\) similar drops of mercury are maintained at \(10 \,V\) each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ....... times that of a smaller drop.JEE Mains 2021 Hard
- A ball of mass \(200\,g\) rests on a vertical post of height \(20\,m\). A bullet of mass \(10\,g\), travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance \(30\,m\) and the bullet at a distance of \(120\,m\) from the foot of the post. The value of initial velocity of the bullet will be \(............m/s\) (if \(\left.g =10 m / s ^2\right)\)JEE Mains 2023 Hard
- Four particles each of mass \(1 \mathrm{~kg}\) are placed at four corners of a square of side \(2 \mathrm{~m}\). Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is_________ \(\mathrm{kgm}^2\).
JEE Mains 2024 Hard - A plane electromagnetic wave of frequency \(100\, MHz\) is travelling in vacuum along the \(x -\) direction. At a particular point in space and time, \(\overrightarrow{ B }=2.0 \times 10^{-8} \hat{ k } T\). (where, \(\hat{ k }\) is unit vector along \(z-\)direction) What is \(\overrightarrow{ E }\) at this point ?JEE Mains 2021 Medium
More PYQs from JEE Mains
- \(S = {\tan ^{ - 1}}\left( {\frac{1}{{{n^2} + n + 1}}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{{{n^2} + 3n + 3}}} \right) + ..... + {\tan ^{ - 1}}\left( {\frac{1}{{1 + \left( {n + 19} \right)\left( {n + 20} \right)}}} \right)\) , then \(tan\,S\) is equal toJEE Mains 2013 Hard
- The formula \(X = 5YZ^2\), \(X\) and \(Z\) have dimensions of capacitance and magnetic field respectively. What are the dimensions of \(Y\) in \(SI\) units?JEE Mains 2019 Hard
- The area of the region given by \(A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\}\) is.JEE Mains 2022 Hard
- The \(I-V\) characteristics of a \(p - n\) junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltages of \(2 \; V\) and \(4 \; V\) respectively, is
JEE Mains 2022 Medium - To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm . The least count of scale is 1 cm . The percentage error in the ratio of EMFs is ___________.JEE Mains 2026 Medium
- Suppose for a differentiable function \(h, h(0)=0\), \(\mathrm{h}(1)=1\) and \(\mathrm{h}^{\prime}(0)=\mathrm{h}^{\prime}(1)=2\). If \(\mathrm{g}(\mathrm{x})=\mathrm{h}\left(\mathrm{e}^{\mathrm{x}}\right) \mathrm{e}^{\mathrm{h}(\mathrm{x})}\), then \(g^{\prime}(0)\) is equal to :JEE Mains 2024 Medium