Assertion: For a point light source, frequency of light emitted is numerically equal to number of photons emitted per second.

Reason: According to wave theory frequency of light wave is equivalent to number of cycles completed per second and wave-particle duality explains the dual nature of electromagnetic waves as a wave or as a corpuscle.

How fast would a rocket have to go relative to an observer for its length to be corrected to $99\%$ of its length at rest? $\left(\mathrm{c}=3\times {10}^8{\mathrm{ms}}^{-1}\right)$

The radii of curvature of the faces of a double convex lens made of glass, are $10 \mathrm{cm}$ and $15 \mathrm{cm}$. Its focal length is $12 \mathrm{cm}$.

$\left(\mathrm{a}\right)$ Find the refractive index of glass

$\left(\mathrm{b}\right)$ Calculate its new focal length if the lens is completely immersed in water ( Refractive index of water is $\frac{4}{3}$)

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of $x$ is ______.

(Given speed of light in free space $=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$ and for the given medium ${\mu }_r=1$)

The following graph depicts the inverse of magnification versus the distance between the object and lens data for a setup. The focal length of the lens used in the setup is

Distance between the object and the lens $\left(\mathrm{m}\right)$