The intensity at spherical surface due to an isotropic point source placed at its center is $I_0$. If its volume is increased by $8$ times, what will be intensity at the spherical surface?
The intensity at spherical surface due to an isotropic point source placed at its center is $I_0$. If its volume is increased by $8$ times, what will be intensity at the spherical surface?
Show Hint
- Increase by $128$ times
- Increase by $8$ times
- Decrease by $4$ times
- Decrease by $8$ times
The Correct Option is C
Solution and Explanation
\[ V \propto R^3 \Rightarrow 8V \Rightarrow R' = 2R \]
Step 2: Relation between intensity and radius.
\[ I \propto \dfrac{1}{R^2} \]
Step 3: Finding new intensity.
\[ I' = \dfrac{I_0}{(2)^2} = \dfrac{I_0}{4} \]
Top Questions on Wave optics
- Which of the following are true for a single slit diffraction? A. Width of central maxima increases with increase in wavelength keeping slit width constant.
B. Width of central maxima increases with decrease in wavelength keeping slit width constant.
C. Width of central maxima increases with decrease in slit width at constant wavelength.
D. Width of central maxima increases with increase in slit width at constant wavelength.
E. Brightness of central maxima increases for decrease in wavelength at constant slit width.
- JEE Main - 2026
- Physics
- Wave optics
- Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ________ cm.
- JEE Main - 2026
- Physics
- Wave optics
- In the Young's double slit experiment the intensity produced by each one of the individual slits is \(I_0\). The distance between two slits is \(2\,\text{mm}\). The distance of screen from slits is \(10\,\text{m}\). The wavelength of light is \(6000\,\text{\AA}\). The intensity of light on the screen in front of one of the slits is ________.
- JEE Main - 2026
- Physics
- Wave optics
- A point source is kept at the center of a spherically enclosed detector. If the volume of the detector is increased by 8 times, the intensity will
- JEE Main - 2026
- Physics
- Wave optics
- When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is ___. ($\tan^{-1}(1.52) = 57.7^\circ$, refractive indices of air and glass are 1.00 and 1.52, respectively.)
- JEE Main - 2026
- Physics
- Wave optics
Questions Asked in JEE Main exam
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]- JEE Main - 2026
- Ray optics and optical instruments
A small block of mass \(m\) slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration \(a_0\). The angle between the inclined plane and ground is \(\theta\) and its base length is \(L\). Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is _______.
- JEE Main - 2026
- General Physics
- Let \(\vec{a} = -\hat{i} + 2\hat{j} + 2\hat{k}\), \(\vec{b} = 8\hat{i} + 7\hat{j} - 3\hat{k}\) and \(\vec{c}\) be a vector such that \(\vec{a} \times \vec{c} = \vec{b}\). If \(\vec{c} \cdot (\hat{i}+\hat{j}+\hat{k}) = 4\), then \(|\vec{a}+\vec{c}|^2\) is equal to:
- JEE Main - 2026
- Vector Algebra
- Let \( \alpha \) and \( \beta \) respectively be the maximum and the minimum values of the function \( f(\theta) = 4\left(\sin^4\left(\frac{7\pi}{2} - \theta\right) + \sin^4(11\pi + \theta)\right) - 2\left(\sin^6\left(\frac{3\pi}{2} - \theta\right) + \sin^6(9\pi - \theta)\right) \). Then \( \alpha + 2\beta \) is equal to :
- JEE Main - 2026
- Statistics
- The crystal field splitting energy of $[Co(oxalate)_3]^3-$ complex is 'n' times that of the $[Cr(oxalate)_3]^3-$ complex. Here 'n' is_______ (Assume $\Delta_0 > P$)}
- JEE Main - 2026
- Solutions