Optical Path Length

Q.

The colours on the soap bubble is due to

1. Interference

2. Polarisation

3. Diffraction

4. Reflection

Q. With what speed should a galaxy move outward with respect to earth so that the sodium$-\text{D}$ line at wavelength $5890\dot{\text{A}}$ is observed at $5896\dot{\text{A}}?$

1. $306\text{km/sec}$
2. $322\text{km/sec}$
3. $296\text{km/sec}$
4. $336\text{km/sec}$

Q. In the ideal double – slit experiment, when a glass – plate $(\mu =1.5)$ of thickness t is introduced in the path of one of the interfering beams $(wave–length\lambda )$, the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass – plate is

1. $2\lambda$
2. $\frac{2\lambda }{3}$
3. $\frac{\lambda }{3}$
4. $\lambda$

Q. In a Young's double slit experiment, the fringes are displaced by a distance $x$ when a glass plate of refractive index $1.5$ is introduced in the path of one of the beams. When this plate is replaced by another plate of same thickness, the shift of fringes is $\left(3/2\right)x$. The refractive index of second plate is

1. $1.75$
2. $1.40$
3. $1.25$
4. $1.67$

Q. 43. The ratio of resolving powers of an optical microscope for two wavelengths 4000 A , and 6000 A is

Q. A transparent slab of thickness d has a refractive index $n\left(z\right)$ that increases with $z$. Here $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_1$ and $n_2$ $(>n_1)$, as shown in the figure. A ray of light incident with angle ${\theta }_i$ from medium 1 and emerges in medium 2 with refraction angle ${\theta }_f$ with lateral displacement $l$.
Which of the following statement(s) is (are) true?

1. $l$ is dependent on $n\left(z\right)$
2. $n_1\sin {\theta }_i=(n_2-n_1)\sin {\theta }_f$
3. $n_1\sin {\theta }_i=n_2\sin {\theta }_f$
4. $l$ is independent of $n_2$

Q.

Monochromatic light of wavelength of 600nm is used in a YDSE. One of the slits is covered by a transparent sheet of thickness $1.8\times {10}^{-5}m$ made of a material of refractive index 1.6. How many fringes will shift due to the introduction of the sheet?

1. 18

2. 12

3. 20

4. 10

Q. Bichromatic light of wavelengths ${\lambda }_1=5000\dot{\text{A}}\text{and}{\lambda }_2=7000\dot{\text{A}}$ are used in $YDSE$. Then,

1. ${14}^{th}$ order maxima of ${\lambda }_1$, will coincide with ${10}^{th}$ order maxima of ${\lambda }_2$.
   
2. ${21}^{st}$ order maxima of ${\lambda }_2$, will coincide with ${15}^{th}$ order maxima of ${\lambda }_1$.
3. ${11}^{th}$ order minima of ${\lambda }_1$, will coincide with $8^{th}$ order minima of ${\lambda }_2$.
4. $3^{rd}$ order minima of ${\lambda }_1$, will coincide with $4^{th}$ order maxima of ${\lambda }_2$

Q.

A microscope is focused on an ink mark on the top of a table. If we place a glass slab 3cm thick on it, how should the microscope be moved to focus the ink spot again? The refractive index of glass slab is 1.5 cm.

1. 2 cm upwards

2. 1 cm downwards

3. 2 cm downward

4. 1 cm upwards

Q. A plate of thickness t made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness t which will make the intensity at the centre of the fringe pattern zero?

1. $(\mu -1)\frac{\lambda }{2}$
   
2. $(\mu -1)\lambda$
   
3. $\frac{\lambda }{2(\mu -1)}$
   
4. $\frac{\lambda }{(\mu -1)}$

Q. Ratio of width of principal maxima to the second order maxima in Fraunhofer single slit diffraction is 1) 4 2) 3 3) 2 4) 1

Q. A double slit experiment is performed with light of wavelength 500 nm. A thin film of thickness 2$\mu$ m and refractive index 1.5 is introduced in the path of the upper beam. The location of the central maximum will:

1. Remain unshifted
2. Shift downward by nearly two fringes
3. Shift upward by nearly two fringes
4. Shift downward by 10 fringes

Q. In YDSE, find the thickness of a glass slab $(\mu =1.5)$ which should be placed before the upper slit $S_1$ so that the central maximum now lies at a point where $5^{th}$ bright fringe was laying earlier (before inserting the slab). Wavelength of light used is $5000\dot{A}$.

1. $5\times {10}^{-6}m$
   
2. $3\times {10}^{-6}m$
   
3. $10\times {10}^{-6}m$
   
4. $5\times {10}^{-5}m$

Q. When a mica sheet of thickness 7 microns and $\mu =1.6$ is placed in the path of one of interfering beams in the $YDSE$, then the central fringe gets at the position of the seventh bright fringe. What is the wavelength of light used ?

1. $6000\stackrel{\circ }{A}$
2. $3000\stackrel{\circ }{A}$
3. $4000\stackrel{\circ }{A}$
4. $2000\stackrel{\circ }{A}$

Q. Assertion:
Thin film such as soap bubble or a thin layer of oil on water shows beautiful colors when illuminated by white light.

Reason:
It happens due to the interference of light reflected from the upper surface of the thin film.

1. Both Assertion and Reason are correct, and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion
3. Assertion is correct, but Reason is incorrect
4. Assertion is incorrect, but Reason is correct

Q. In young's double-slit experiment, we get $60$ fringes in the field of view of monochromatic light of wavelength $4000\mathring{\text{A}}.$ If we use monochromatic light of wavelength $6000\mathring{\text{A}},$ then the number of fringes obtained in the same field of view are

1. $60$
2. $90$
3. $40$
4. $15$

Q. An electromagnetic wave of wavelength ${\lambda }_0$ (in vacuum) passes from $P$ towards $Q$ crossing three different media of refractive index $\mu ,2\mu$ and $3\mu$ respectively as shown in figure. ${\varphi }_P$ and ${\varphi }_Q$ are the phase of the wave at point $P$ and $Q$. Find the phase difference ${\varphi }_Q-{\varphi }_P$ [Take: $\mu =1$]

1. $0$
2. $\frac{\pi }{2}$
3. $\pi$
4. $\frac{\pi }{4}$

Q.

Find the angular separation between th econsecutive bright fringes in a young's doubel slit experiment with blue- green light of wavelength 500 nm. The separation between the slits is $2.0\times {10}^{-3}m$

Q.

Suppose that intensity of a laser is $\frac{315}{\mathrm{\pi }}W{m}^{-2}$. The RMS electric field, in units of V/m associated with this source is close to the nearest integer is __________. $\left({\epsilon }_{\circ }=8·86\times {10}^{-12}{C}^{2}N{m}^{-2},c=3·0\times {10}^{8}m{s}^{-1}\right)$

Q. In a YDSE, light of wavelength $\lambda =5000\stackrel{\circ }{A}$ is used, which emerges in phase from two slits a distance $d=3\times {10}^{-7}m$ apart. A transparent sheet of thickness $t=1.5\times {10}^{-7}m$, refractive index $n=1.17$, is placed over one of the slits. Where does the central maxima of the interference now appear from the center of the screen? (Find the value of y?)

1. $\frac{D(\mu -1)t}{2d}$
2. $\frac{2D(\mu -1)t}{d}$
3. $\frac{D(\mu +1)t}{d}$
4. $\frac{D(\mu -1)t}{d}$

Q. An air bubble in a glass slab $(\mu =1.5)$ appears $3cm$ deep when viewed from one face and $4cm$ when viewed from opposite face, then real thickness of glass slab is

1. $9cm$
2. $9.5cm$
3. $8.5cm$
4. $10.5cm$

Q. What will be the angular width of central maxima in Fraunhoffer diffraction when light of wavelength $6000\mathring{A}$ is used and slit width is $12\times {10}^{-5}cm$.

1. $2rad$
2. $3rad$
3. $8rad$
4. $1rad$

Q. A triangular prism of glass is shown in the figure. A ray incident normally to the one face is totally reflected if $\theta$ is ${45}^{\circ }.$ The refractive index of glass is:

1. $\mu <1.41$
2. $\mu =1.41$
3. $\mu >1.41$
4. None

Q.

A flint glass and a crown glass are fitted on the two slits of a double slit apparatus. The thickness of the strips is 0.40 mm and the separation between the slits is 0.12 cm. The refractive index of flint glass and crown glass are 1.62 and 1.52 respectively for the light of wavelength 480 nm which is used in the experiment. The interference is observed on a screen a distance one meter away

(a) What would be the fringe-width?

(b) At what distance from the geometrical centre will the nearest maximum be located?

Q.

Light is confined within the core of a simple optical fiber by:

1. refraction

2. reflection from the fiber's plastic coating.

3. total internal reflection at the outer edge of the cladding.

4. total internal reflection at the core cladding boundary.

Q. A thin film of soap solution of refractive index $\mu$ and thickness t appears shining by a normal reflected light wavelength $\lambda$ then t can be

1. $\frac{\lambda }{2\mu }$
2. $\frac{2\lambda }{3\mu }$
3. $\frac{3\lambda }{8\mu }$
4. $\frac{6\lambda }{8\mu }$

Q. In YDSE, source is red light of wavelength $7\times {10}^{-7}m$. When a thin glass plate of refractive index 1.5 is put in the path of one of the interfering beams, the central bright fringe shifts by ${10}^{-3}$ m to the position previously occupied by the $5^{th}$ bright fringe. Find the thickness of the plate. When the source is now changed to green light of wavelength $5\times {10}^{-7}m$, the central fringe shifts to a position initially occupied by the $6^{th}$ bright fringe due to red light. Find the refractive index of glass for the green light.

1. 1.6
   
2. 1.8
   
3. 2
4. None of these

Q. In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?

Q. Of the two slits producing interference in Young’s experiment, one is covered with glass so that light intensity passing is reduced to 50%. Which of the following is correct?

1. Intensity of bright fringe decreases and that of dark fringe increases
2. Intensity of fringes remains unaltered
3. Intensity of bright fringe increases and that of dark fringe decreases
4. Intensity of both bright and dark fringes decreases

Q. An observer is moving with one-third of the speed of light towards a stationary microwave source emitting waves at frequency $8\text{GHz}$. What is the frequency of the microwave measured by the observer?

1. $8\text{GHz}$
2. $8\sqrt{3}\text{GHz}$
3. $8\sqrt{2}\text{GHz}$
4. $\frac{8}{3}\text{GHz}$