CPET Physics Quiz-3 - Ashirbad Mohanty

1. The dispersion relation for electromagnetic waves travelling in a plasma is given as $\omega^2=c^2 k^2 +\omega_p^2$, where $c$ and $\omega_p$ are constants. In this plasma, the group velocity is:

proportional to but not equal to the phase velocity

inversely proportional to the phase velocity

equal to the phase velocity

a constant

2. For dispersive medium, group velocity $(v_g)$ and phase velocity $(v_p)$ are related as

$v_g=v_p + \lambda \frac{dv_p}{d\lambda}$

$v_g=v_p - \lambda \frac{dv_p}{d\lambda}$

$v_g=v_p - \frac{1}{\lambda} \frac{dv_p}{d\lambda}$

$v_g=v_p + \frac{1}{\lambda} \frac{dv_p}{d\lambda}$

3. In Newton's rings experiment, the diameter of 10th dark ring due to wavelength $6000 A^0 $ in air is $0.5 cm$. The radius of curvature of the lens is

$1.04 m$

$2.04 m$

$3.04 m$

$4.04 m$

4. The radius of the first half period zone in a zone plane behaving like a convex lens of focal length $60 cm$ for light of wavelength $6000 A^0$ is

$0.3 mm$

$0.4 mm$

$0.5 mm$

$0.6 mm$

5. In Newton’s rings experiment, the diameter of the 15th ring was found to be $0.59 cm$ and that of the 5th ring was $0.336 cm$. If the radius of the planoconvex lens is $100 cm$, the wavelength of light used is

$5880 A^0$

$6880 A^0$

$7880 A^0$

$8880 A^0$

6. Plane polarized light passes through a calcite plate with its optic axis parallel to the faces. The thickness of the plate for which the emergent beam will be plane polarized is (Given $\mu_0=1.6584$, $\mu_e=1.4864$ and wavelength of light is $5000 A^0$)

$4.45 \mu m$

$3.45 \mu m$

$2.45 \mu m$

$1.45 \mu m$

7. Two cohorent monochromatic sources of light have intensities in the ratio $\alpha:1$. If $I_M$ and $I_m$ denote the maximum and minimum intensities in the interference pattern, then $\frac{I_M+I_m}{I_M-I_m}$ will be equal to

$\frac{1+\alpha}{2\sqrt{\alpha}}$

$\frac{1-\alpha}{2\sqrt{\alpha}}$

$\frac{\alpha}{2\sqrt{\alpha}}$

$\frac{-\alpha}{2\sqrt{\alpha}}$

8. If $\alpha$ and $\beta$ represent the longitudinal and transverse magnifications respectively for a coaxial optical system placed in an uniform, homogeneous and isotropic medium, then

$\alpha=-\beta^2$

$\alpha^2=\beta$

$\alpha=\frac{1}{\beta}$

$\alpha=\frac{1}{\beta^2}$

9. The thickness of a calcite plate which would convert plane polarized light into circularly polarized light is (given $\mu_0=1.658$, $\mu_e= 1.486$ and wavelength of light is $5890 A^0$)

$1.856 \mu m$

$2.856 \mu m$

$0.856 \mu m$

$3.856 \mu m$

10. An object of $2 cm$ height is placed at a distance of $30 cm$ in front of a concave mirror with radius of curvature $40 cm$. The height of the image is

$4 cm$

$8 cm$

$2 cm$

$1 cm$

11. A convex lens of focal length $24 cm$ and refractive index $1.5$ is totally immersed in water of refractive index $1.33$, its focal length in water is

$96 cm$

$48 cm$

$24 cm$

$12 cm$

12. Two thin convex lenses having focal lengths $20 cm$ and $5 cm$ are coaxial and separated by a distance of $10 cm$. The equivalent focal length is

$6.67 cm$

$8.96 cm$

$2.36 cm$

$4.73 cm$

13. Green light of wavelength $5100 A^0$ from a narrow slit is incident on a double slit. If the overall separation of 10 fringes on a screen $200 cm$ away is $2 cm$, the slit separation is

$0.05 cm$

$0.1 cm$

$1.5 cm$

$0.02 cm$

14. A thin sheet of a transparent material of refractive index, $\mu=1.50$ is placed in the path one of the interfering beams in a biprism experiment with a monochromatic source of wavelength, $\lambda =5000 A^0$ . The central fringe shifts to a position originally occupied by 10th bright fringe. The thickness of the sheet is

$10^{-5} m$

$1.5 \times 10^{-5} m$

$0.5 \times 10^{-5} m$

$2 \times 10^{-5} m$

15. When unpolarized light of intensity $I_0$ is incident on a polarizer, the intensity of light transmitted through the polarizer is

$I_0/2$

$I_0/4$

$I_0/8$

$I_0$

16. The width of one of the two slits in a Young's double slit experiment is double of the other slit. Assuming that the amplitude of the light coming from a slit is proportional to the slit width, the ratio of maximum to minimum intensity in the interference pattern is

9:1

3:1

2:1

4:1

17. A biconvex lens has radii of curvature $20 cm$ each. The refractive index of the material of the lens is 1.5, its focal length is

$20 cm$

$10 cm$

$40 cm$

$30 cm$

18. Three sinusoidal waves have the same frequency with amplitude $A$, $A/2$ and $A/3$ while their phase angles are $0$, $\pi/2$ and $\pi$ respectively. The amplitude of the resultant wave is

$\frac{5A}{6}$

$\frac{7A}{6}$

$\frac{6A}{5}$

$\frac{6A}{7}$

19. Light is incident from a medium of refractive index $n=1.5$ onto vacuum. The smallest angle of incidence for which the light is not transmitted into vacuum is

$\sin^{-1}(\frac{1}{1.5})$

$\sin^{-1}(\frac{2}{1.5})$

$\sin^{-1}(1.5)$

$\sin^{-1}(2.5)$

20. For achromatic combination of a system of two thin lenses made of same material with optical powers $P_1$ and $P_2$ respectively, the separation distance of the two lenses must be

$\frac{P_1+P_2}{2P_1 P_2}$

$\frac{P_1+P_2}{P_1 P_2}$

$\frac{P_1+P_2}{2}$

$P_1+P_2-2P_1P_2$

21. Two objects at a distance $s$ apart are viewed by a telescope when they are at a distance $z$ from the telescope through a light of wavelength $\lambda$. If the telescope can just resolve the two objects, the radius of its objective lens would be

$\frac{0.61 \lambda z}{s}$

$\frac{1.22 \lambda z}{s}$

$\frac{\lambda z}{s}$

$\frac{\lambda z}{2s}$

22. Two thin lenses of focal lengths $f_1$ and $f_2$ are to be placed in contact with each other to form an achromat. If the dispersive powers of these lenses are $\omega_1$ and $\omega_2$ respectively, then the focal lengths $f_1$ and $f_2$ must be such that

$\frac{f_1}{f_2}=-\frac{\omega_1}{\omega_2}$

$\frac{f_1}{f_2}=\frac{\omega_1}{\omega_2}$

$f_1 \omega_1+f_2 \omega_2=0$

$f_1 \omega_2+f_2 \omega_1=0$

23. A double slit is illuminated by light containing two wavelengths $4800 A^0$ and $5000 A^0$ to give an interference pattern on a screen. Then the lowest order $n$ for which a maximum of one wavelength will fall exactly on the minimum of the other is

$n=2$

$n=1$

$n=3$

$n=4$

24. An unpolarized monochromatic light passing through a polarizer is incident on a quarter wave plate. The quarter wave plate is placed in such a way that the electric field of the plane polarized wave makes an angle $45^0$ with the optic axis of the quarter wave plate. Then the nature of the light after passing through the quarter wave plate would be

circularly polarized

elliptically polarized

plane polarized

unpolarized

25. In a monochromatic beam of light, the electric field is given by $\vec{E}(\vec{r},t)=[8\hat{y}\sin(kx-\omega t + 65^0) + 8\hat{z}\sin(kx-\omega t-25^0)] V/m$. The beam of light is

plane polarized

elliptically polarized

unpolarized

circularly polarized