Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is _____ cm.
Correct Answer: 30
Solution and Explanation
The refraction at a spherical surface is governed by the equation: \[ \frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}, \] where:
\( \mu_1 = 1.0 \) (refractive index of the rarer medium),
\( \mu_2 = 1.5 \) (refractive index of the denser medium),
\( u = -15 \, \text{cm} \) (object distance, negative as it is measured opposite to the direction of incident light),
\( R = +30 \, \text{cm} \) (radius of curvature, positive as the center of curvature lies in the denser medium),
\( v \) is the image distance to be determined.
Substitute the values into the equation: \[ \frac{1.5}{v} - \frac{1.0}{-15} = \frac{1.5 - 1.0}{30}. \]
Simplify: \[ \frac{1.5}{v} + \frac{1}{15} = \frac{0.5}{30}. \] \[ \frac{1.5}{v} = \frac{1}{60} - \frac{1}{15}. \]
Simplify further: \[ \frac{1.5}{v} = \frac{1 - 4}{60} = \frac{-3}{60}. \] \[ \frac{1.5}{v} = -\frac{1}{20}. \] Solve for \( v \): \[ v = -\frac{1.5 \cdot 20}{1} = -30 \, \text{cm}. \] The negative sign indicates that the image is formed on the opposite side of the refracting surface, i.e., in the denser medium.
Final Answer: The distance of the image from the pole of the surface is: \[ \boxed{30 \, \text{cm}}. \]
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- 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 rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
Top JEE Main Light - Reflection and Refraction Questions
- The ratio of intensities of two coherent sources is 1:9. The ratio of the maximum to the minimum intensities is:
- Two plane polarized light waves combine at a certain point whose electric field components are $ E_1 = E_0 \sin(\omega t) $ $ E_2 = E_0 \sin(\omega t + \frac{\pi}{3}) $ Find the amplitude of the resultant wave.
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- 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 rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.