Wave Optics · JEE Main previous year questions

A single slit of width b is illuminated by a coherent monochromatic light of wavelength $\lambda$. If the second and fourthminima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)

1. A.$1.5\mathrm{cm}$
2. B.$3.0\mathrm{cm}$
3. C.$4.5\mathrm{cm}$
4. D.$6.0\mathrm{cm}$

The box of a pin hole camera, of length $L$, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $\lambda$ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $b_{\min }$) when :

1. A.$a=\sqrt{\lambda L}\text{ and }{b}_{\min }=\sqrt{4\lambda L}$
2. B.$a=\frac{{\lambda }^2}{L}\text{ and }{b}_{\min }=\sqrt{4\lambda L}$
3. C.$a=\frac{{\lambda }^2}{L}\text{ and }{b}_{\min }=\left(\frac{2{\lambda }^2}{L}\right)$
4. D.$a=\sqrt{\lambda L}\text{ and }{b}_{\min }=\left(\frac{2{\lambda }^2}{L}\right)$

Two beams, $A$ and $B$, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through $30^{\circ }$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_A$ and $I_B$ respectively, then $\frac{I_A}{I_B}$ equals:

1. A.$3$
2. B.$\frac{3}{2}$
3. C.$1$
4. D.$\frac{1}{3}$

In Young's double slit interference experiment, the slit widths are in the ratio $1:25$. Then the ratio of intensity at the maxima and minima in the interference pattern is

1. A.$3:2$
2. B.$1:25$
3. C.$9:4$
4. D.$1:5$

The first diffraction minimum due to the single slit diffraction is seen at $\theta =30^{\circ }$ for a light of wavelength $5000\mathring{\mathrm{A}}$ falling perpendicularly on the slit. The width of the slit is

1. A.$2.5\times 10^{-5}\mathrm{cm}$
2. B.$1.25\times 10^{-5}\mathrm{cm}$
3. C.$10\times 10^{-5}\mathrm{cm}$
4. D.$5\times 10^{-5}\mathrm{cm}$

The maximum number of possible interference maxima for slit separation equal to $1.8\lambda$, where $\lambda$ is the wavelength of light used, in a Young's double slit experiment is

1. A.zero
2. B.3
3. C.infinite
4. D.5

In a Young's double slit experiment with light of wavelength $\lambda$, fringe pattern on the screen has fringe width $\beta$. When two thin transparent glass (refractive index $\mu$) plates of thickness $t_1$ and $t_2$ ($t_1>t_2$) are placed in the path of the two beams respectively, the fringe pattern will shift by a distance

1. A.$\frac{\beta (\mu -1)}{\lambda }\left(\frac{t_1}{t_2}\right)$
2. B.$\frac{\mu \beta }{\lambda }\frac{t_1}{t_2}$
3. C.$\frac{\beta (\mu -1)}{\lambda }(t_1-t_2)$
4. D.$(\mu -1)\frac{\lambda }{\beta }(t_1+t_2)$

Two polaroids have their polarizing directions parallel so that the intensity of a transmitted light is maximum. The angle through which either polaroid must be turned if the intensity is to drop by one-half is

1. A.$135^{\circ }$
2. B.$90^{\circ }$
3. C.$120^{\circ }$
4. D.$180^{\circ }$

A mixture of light, consisting of wavelength $590nm$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is :

1. A.$885.0nm$
2. B.$442.5nm$
3. C.$776.8nm$
4. D.$393.4nm$

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

1. A.circle
2. B.hyperbola
3. C.parabola
4. D.straight line

If $I_0$ is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

1. A.$4I_0$
2. B.$2I_0$
3. C.$\frac{I_0}{2}$
4. D.$I_0$

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

1. A.$\frac{1}{4}{I}_0$
2. B.$\frac{1}{2}{I}_0$
3. C.$I_0$
4. D.$\mathrm{zero}$

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $n$) is :

1. A.${\tan }^{-1}(1/n)$
2. B.${\sin }^{-1}(1/n)$
3. C.${\sin }^{-1}(n)$
4. D.${\tan }^{-1}(n)$

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment, is :

1. A.three
2. B.five
3. C.infinite
4. D.zero

Wavelengths of light used in an optical instrument are ${\lambda }_1=4000\mathring{A}$ and ${\lambda }_2=5000\mathring{A}$, then ratio of their respective resolving powers (corresponding to ${\lambda }_1$ and ${\lambda }_2$ ) is :

1. A.$16:25$
2. B.$9:1$
3. C.$4:5$
4. D.$5:4$