Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$ Assertion A : The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2}\mathrm{mgR}$, where R is the radius of earth. Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface. In the light of the above statements, choose the correct answer from the options given below

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below :

A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R) : The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below :

The width of one of the two slits in Young's double slit experiment is d while that of the other slit is $x\mathrm{d}$. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is $9: 4$ then what is the value of $x$ ? (Assume that the field strength varies according to the slit width.)

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $P_1$ and $P_2$ are orthogonal to each other. The polarizer $P_3$ covers both the slits with its transmission axis at $45^{\circ }$ to those of $P_1$ and $P_2$. An unpolarized light of wavelength $\lambda$ and intensity $I_0$ is incident on $P_1$ and $P_2$. The intensity at a point after $P_3$ where the path difference between the light waves from $s_1$ and $s_2$ is $\frac{\lambda }{3}$, is

Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be:

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case:

A light wave is propagating with plane wave fronts of the type $x+y+z=$ constant. Th angle made by the direction of wave propagation with the $x$-axis is :

Two plane polarized light waves combine at a certain point whose electric field components are $$\begin{array}{rl}& E_1=E_0\mathrm{Sin}\omega t\\ & E_2=E_0\mathrm{Sin}\left(\omega t+\frac{\pi }{3}\right)\end{array}$$ Find the amplitude of the resultant wave.

Two polarisers $P_1$ and $P_2$ are placed in such a way that the intensity of the transmitted light will be zero. A third polariser $P_3$ is inserted in between $P_1$ and $P_2$, at particular angle between $P_2$ and $P_3$. The transmitted intensity of the light passing the through all three polarisers is maximum. The angle between the polarisers $P_2$ and $P_3$ is :

In a Young's double slit experiment, the slits are separated by 0.2 mm . If the slits separation is increased to 0.4 mm , the percentage change of the fringe width is :

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

A monochromatic light of frequency $5\times 10^{14}\mathrm{Hz}$ travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

A capacitor, $C_1=6\mu F$ is charged to a potential difference of $V_0=5V$ using a 5V battery. The battery is removed and another capacitor, $C_2=12\mu F$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached.

An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity $10^6\mathrm{m}/\mathrm{s}$. If the magnitude of the electric field between the plates is $9.1\mathrm{V}/\mathrm{cm}$, then the vertical component of velocity of electron is (mass of electron $=9.1\times 10^{-31}\mathrm{kg}$ and charge of electron $=1.6\times 10^{-19}\mathrm{C}$ )

A parallel-plate capacitor of capacitance $40\mu \mathrm{F}$ is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant $\mathrm{K}=2$. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M},\mathrm{L},\mathrm{T}$ and $C$ stand for unit of mass, length, time and charge,