Diffraction through Circular Slits

Q. A diffraction pattern is obtained using a beam of red light. What happens if the red light is replaced by blue light?

1. No change
2. Diffraction bands become narrower and crowded together.
3. Band become broader and farther apart.
4. Bands disappear altogether.

Q. In a $YDSE$ experiment with $d=1\text{mm}$ and $D=1\text{m}$, two slabs with refractive index and thickness $(t_1=1\mu \text{m},{\mu }_1=3)$ and $(t_2=0.5\mu \text{m},{\mu }_2=2)$ are introduced in front of upper and lower slits respectively, The shift in the fringe pattern will be

1. $1.5\text{mm}$ downwards
2. $1.5\text{mm}$ upwards
3. $2.5\text{mm}$ upwards
4. $2\text{mm}$ downwards

Q. A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength $5\times {10}^{-5}$ cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is:

1. 0.15 cm
2. 0.10 cm
3. 0.20 cm
4. 0.25 cm

Q. The angular width of central maxima in the Fraunhofer diffraction pattern is measured. The slit is illuminated by the light of wavelength $6000\mathring{A}$ If the slit is illuminated by a light of another wavelength, angular width decreases by 30%. The wavelength of light used is :

1. $3500\mathring{A}$
2. $4200\mathring{A}$
3. $4700\mathring{A}$
4. $6000\mathring{A}$

Q. Is parallax approximation and paraxial approximation same or different? If different then what is actually parallax approximation?

Q. In Young's double -slit experiment, the intensity of light at a point on the screen, where the path difference is $\lambda$ , is I. The intensity of light at a point where the path difference becomes $\frac{\lambda }{3}$ is

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

Q. An astronomical telescope has focal lengths $100$ & $10$cm of objective and eyepiece lens respectively when final image is formed at least distance of distinct vision, magnification power of telescope will be,

1. -14
2. -17
3. -19
4. -15

Q. Read the statements A and B and mark the correct option.
Statement A: In Fresnel diffraction phenomenon, the source or screen or both are at finite distances from the aperture.
Statement B: In Fraunhoffer diffraction, lenses are used to modify the incoming light.

1. Both A and B are correct
2. A is correct and B is wrong
3. A is wrong and B is correct
4. Both A and B are wrong

Q. Two light rays having the same wavelength in vacuum are in phase initially. Then, the first ray travels a path $L_1$ through a medium of refractive index ${\mu }_1$ while the second ray travels a path $L_2$ through a medium of refractive index ${\mu }_2$. The two waves are then combined to observe interference. The Phase difference between the two waves is

1. $\frac{2\pi }{\lambda }(\frac{L_1}{{\mu }_1}-\frac{L_2}{{\mu }_2})$
2. $\frac{2\pi }{\lambda }(L_2-L_1)$
3. $\frac{2\pi }{\lambda }({\mu }_1{L}_1-{\mu }_2{L}_2)$
4. $\frac{2\pi }{\lambda }({\mu }_2{L}_1-{\mu }_1{L}_2)$

Q.

What is the shape of the wavefront in each of the following cases:

(a) Light diverging from a point source.

(b) Light emerging out of a convex lens when a point source is placed at its focus.

(c) The portion of the wavefront of light from a distant star intercepted by the Earth.

Q. A thin converging lens is made up of a glass of refractive index $1.5$. It acts like a concave lens of focal length $50$ cm when immersed in a liquid of refractive index $\left(\frac{15}{8}\right)$ The focal length of the converging lens in air is (in m)

1. $0.15$
2. $0.20$
3. $0.25$
4. $0.40$

Q. The focal length of the objective and the eye piece of a telescope are 50 cm and 5 cm respectively.If the telescope is focused for distinct vision on a distant scale 2m from its objective, then its magnifying power for near point will be :

1. $-4$
2. $8$
3. $-8$
4. $-2$

Q. A linear aperture whose width is $0.02cm$ is placed immediately in front of a lens of focal length $60cm$. The aperture is illuminated normally by a parallel beam of wavelength $5\times {10}^{-5}cm$. The distance of the first dark band of the diffraction pattern from the centre of the screen is

1. $0.12cm$
2. $0.15cm$
3. $0.25cm$
4. $0.20cm$

Q. In Fraunhoffer diffraction the

1. Source of light and the screen appear to be at infinite distance from the slit
2. The wavefront’s involved in this case are plane
3. Convex lenses are used to focus the diffraction fringes on the screen
4. All the above

Q. The diameter of the objective lens of microscope makes an angle ${}^{\prime }\beta {}^{\prime }$ at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index 'n'. Then the resolving power of the microscope.

1. Increases with increasing value of $nsin2\beta$
2. Increases with decreasing value of $\beta$
3. Increases with increasing value of $\frac{1}{nsin2\beta }$
4. Increases with decreasing value of $n$

Q. Calculate the wavelength of light used in an interference experiment from the following data: Fringe width $=0.03cm$. Distance between slits and eyepiece through which the interference pattern is observed is $1m$. Distance between the images of the virtual source when a convex lens of focal length $16cm$ is used at a distance of $80cm$ from the eyepiece is $0.8cm$.

1. $6000\mathring{A}$
2. $0.00006\mathring{A}$
3. $6000cm$
4. $0.00006m$

Q. Diameter of human eye lens is 2 million. What will be the minimum distance between two points, to resolve them, which are situated at a distance of 50 m from the eye. The wavelength of the light is 5000 angstrom.

1. $2.32m$
2. $4.28mm$
3. $1.25cm$
4. $12.48cm$

Q. Match List – I with List –II (b is size of the object interacting with light; `I' is the distance between the object and the screen; $\lambda$ is the wavelength of the light)
$\begin{array}{cc}List-I& List-II\\ a)\frac{b^2}{1}\lambda \ll 1& e)Theapproximationofgeometricalopticsisapplicable\\ b)\frac{b^2}{1}\lambda \approx 1& f)Fraunhofferdiffractionisobserved\\ c)\frac{b^2}{1}\lambda \gg 1& g)Fresneldiffractionisobserved\end{array}$

1. 
   $a–g,b–f,c–e$
2. 
   $a-g,b-e,c-f$
3. $a-e,b-g,c-f$
4. $a-f,b-g,c-e$

Q. An angular magnification of 30 is desired using an objective of focal length 1.25 cm and eye-piece of focal length 5.0 cm. To set up the microscope the distance between the lenses is :

1. 3.6 cm
2. 6.6 cm
3. 13.75 cm
4. 7.75 cm

Q. Match List – I with List –II (b is size of the object interacting with light; `I' is the distance between the object and the screen; $\lambda$ is the wavelength of the light)
$\begin{array}{cc}List-I& List-II\\ a)\frac{b^2}{1}\lambda \ll 1& e)Theapproximationofgeometricalopticsisapplicable\\ b)\frac{b^2}{1}\lambda \approx 1& f)Fraunhofferdiffractionisobserved\\ c)\frac{b^2}{1}\lambda \gg 1& g)Fresneldiffractionisobserved\end{array}$

1. 
   $a–g,b–f,c–e$
2. 
   $a-g,b-e,c-f$
3. $a-e,b-g,c-f$
4. $a-f,b-g,c-e$

Q. Assertion :Focal length of an equiconvex lens of $\mu =3/2$ is equal to radius of curvature of each surface. Reason: It follows from $\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$

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. Both Assertion and Reason are incorrect

Q. A thin bi-convex lens of focal length $20cm$ is made of glass of refractive index $1.5$. When it is dipped in a liquid of refractive index $\frac{9}{8}$, it acts as a:

1. convex lens of focal length $150cm$
2. concave lens of focal length $30cm$
3. concave lens of focal length $15cm$
4. convex lens of focal length $30cm$

Q. Read the statements A and B and mark the correct option.
Statement A: In Fresnel diffraction phenomenon, the source or screen or both are at finite distances from the aperture.
Statement B: In Fraunhoffer diffraction, lenses are used to modify the incoming light.

1. Both A and B are correct
2. A is correct and B is wrong
3. A is wrong and B is correct
4. Both A and B are wrong

Q. In Fraunhoffer diffraction the

1. The wavefront’s involved in this case are plane
2. Source of light and the screen appear to be at infinite distance from the slit
3. All the above
4. Convex lenses are used to focus the diffraction fringes on the screen

Q. A wire gauge is illuminated with blue light and a convex lens forms a sharp image of it on a screen. If now the wire gauge is illuminated with red light, to get a sharp image again the screen must be :

1. moved towards the lens
2. moved away from the lens
3. placed there itself
4. moved to infinity

Q.

What is the shape of the wavefront in each of the following cases:
(a) Light diverging from a point source.

(b) Light emerging out of a convex lens when a point source is placed at its focus.

(c) The portion of the wavefront of light from a distant star intercepted by the Earth.

Q. Read the statements A and B and mark the correct option.
Statement A: In Fresnel diffraction phenomenon, the source or screen or both are at finite distances from the aperture.
Statement B: In Fraunhoffer diffraction, lenses are used to modify the incoming light.

1. Both A and B are correct
2. A is correct and B is wrong
3. A is wrong and B is correct
4. Both A and B are wrong

Q. Find the right condition(s) for Fraunhoffer diffraction due to a single slit.

1. Source is at infinite distance and the incident beam has converged at the slit.
2. Source is near to the slit and the incident beam is parallel.
3. Source is at infinity and the incident beam is parallel.
4. Source is near to the slit and the incident beam has converged at the slit.

Q. Two thin plano-concave lenses each made of glass of refractive index 1.5 have of curvature 10 cm. If space between lens is filled with oil of refractive index $\frac{8}{7}$ as shown in figure, then magnitude of focal length of the combination will be

1. 18 cm
2. 21 cm
3. -14 cm
4. 15 cm

Q. A beam of light passes from medium $1$ to medium $2$ to medium $3$ as shown in Fig. What may be concluded about the three indices of refraction, $n_1,n_2$ and $n_3$?

1. $n_3>n_1>n_2$
2. $n_1>n_3>n_2$
3. $n_2>n_3>n_1$
4. $n_2>n_1>n_3$