26. A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct ?

1. 1. The angular width of the central maximum of the diffraction pattern will increase.

   
   
   

   2. The angular width of the central maximum will decrease.

   
   
   

   3. The angular width of the central maximum will be unaffected.

   
   
   

   4. Diffraction pattern is not observed on the screen in case of electrons.

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Angular width,
   

   θ =	Y	=	nλD
   	D		dD

   
   

   		∴ Y =	Dλ
   			d

   
   

   So, θ =	λ	, v ↑ λ ↓ θ ↓
   	d

   
   [For central maxima n = 1] ​
   Hence, with increase in speed of electrons angular width of central maximum decreases.

   Correct Option: B

   
   Angular width,
   

   θ =	Y	=	nλD
   	D		dD

   
   

   		∴ Y =	Dλ
   			d

   
   

   So, θ =	λ	, v ↑ λ ↓ θ ↓
   	d

   
   [For central maxima n = 1] ​
   Hence, with increase in speed of electrons angular width of central maximum decreases.

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27. A parallel beam of light of wavelength λ is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the second minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of slit is

1. 1. πλ

   
   
   

   2. 2π

   
   
   

   3. 3π

   
   
   

   4. 4π

   
   
   

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1. View Hint View Answer Discuss in Forum

   Conditions for diffraction minima are ​Path diff. Δx = nλ and Phase diff. δλ = 2nπ ​
   Path diff. = nλ = 2λ
   Phase diff. = 2nπ = 4π (∵ n =2)

   Correct Option: D

   Conditions for diffraction minima are ​Path diff. Δx = nλ and Phase diff. δλ = 2nπ ​
   Path diff. = nλ = 2λ
   Phase diff. = 2nπ = 4π (∵ n =2)

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28. The angular resolution of a 10 cm diameter telescope at a wavelength of 5000 Å is of the order of

1. 1. 10⁶ rad

   
   
   

   2. 10^–2 rad

   
   
   

   3. 10^–2 rad

   
   
   

   4. 10^–2 rad

   
   
   

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1. View Hint View Answer Discuss in Forum

   δφ = 1.22	λ	= 1.22	5000 × 10-10	= 1.6 × 10-6
   	D		10 × 10-2

   
   ∴ Order = 10^-6

   Correct Option: D

   δφ = 1.22	λ	= 1.22	5000 × 10-10	= 1.6 × 10-6
   	D		10 × 10-2

   
   ∴ Order = 10^-6

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29. A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of 50 m. The diameter of the eye-lens of the observer is 2 mm. Which of the following is the least value of d, so that the marks can be seen as separate ? The mean wavelength of visible light may be taken as 5000 Å.

1. 1. 1.25 m

   
   
   

   2. 12.5 cm

   
   
   

   3. 1.25 cm

   
   
   

   4. 2.5 mm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Angular limit of resolution of eye,
   

   θ =	λ
   	d

   
   where, d is diameter of eye lens. ​Also, if y is the minimum separation between two objects at distance D from eye then
   

   θ =	y
   	D

   
   

   ⇒	y	=	λ	⇒ y =	λD	.....(1)
   	D		d		d

   
   Here, wavelength λ = 5000 Å = 5 × 10^-7m
   ​D = 50 m ​
   Diameter  of eye lens = 2 mm = 2 × 10^-3m
   From eq. (1), minimum separation is
   

   y =	5 × 10-7 × 50	= 12.5 × 10-3 m = 12.5cm
   	2 × 10-3

   Correct Option: B

   Angular limit of resolution of eye,
   

   θ =	λ
   	d

   
   where, d is diameter of eye lens. ​Also, if y is the minimum separation between two objects at distance D from eye then
   

   θ =	y
   	D

   
   

   ⇒	y	=	λ	⇒ y =	λD	.....(1)
   	D		d		d

   
   Here, wavelength λ = 5000 Å = 5 × 10^-7m
   ​D = 50 m ​
   Diameter  of eye lens = 2 mm = 2 × 10^-3m
   From eq. (1), minimum separation is
   

   y =	5 × 10-7 × 50	= 12.5 × 10-3 m = 12.5cm
   	2 × 10-3

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30. In a Fresnel biprism experiment, the two positions of lens give separation between the slits as 16 cm and 9 cm respectively. What is the actual distance of separation?

1. 1. 12.5 cm

   
   
   

   2. 12 cm

   
   
   

   3. 13 cm

   
   
   

   4. 14 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Separation between slits are (r₁= 16) cm and (r₂= 9) cm.
   Actual distance of separation
   √r₁r₂ = √16 × 9 = 12 cm

   Correct Option: B

   Separation between slits are (r₁= 16) cm and (r₂= 9) cm.
   Actual distance of separation
   √r₁r₂ = √16 × 9 = 12 cm

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