16. Time taken by sunlight to pass through a window of thickness 4 mm whose refractive index
    

    is	3	is
    	2

1. 1. 2 × 10^–4 sec

   
   
   

   2. 2 × 10⁸ sec

   
   
   

   3. 2 × 10^–11 sec

   
   
   

   4. 2 × 10¹¹ sec

   
   
   

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1. View Hint View Answer Discuss in Forum

   vg =	c	=	3 × 108			= 2 × 108 m / s
   	μ			3
   				2

   
   

   t =	x	=	4 × 10-3	= 2 × 10-11 s
   	vg		2 × 108

   
   
   

   Correct Option: C

   vg =	c	=	3 × 108			= 2 × 108 m / s
   	μ			3
   				2

   
   

   t =	x	=	4 × 10-3	= 2 × 10-11 s
   	vg		2 × 108

   
   
   

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17. Green light of wavelength 5460 Å is incident on an air-glass interface. If the refractive index of glass is 1.5, the wavelength of light in glass would be (c = 3 × 108 ms^–1 )

1. 1. 3640 Å

   
   
   

   2. 5460 Å

   
   
   

   3. 4861 Å

   
   
   

   4. none of the above

   
   
   

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1. View Hint View Answer Discuss in Forum

   λg =	λa	=	5460	= 3640 Å
   	μ		1.5

   
   

   Correct Option: A

   λg =	λa	=	5460	= 3640 Å
   	μ		1.5

   
   

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18. A beam of monochromatic light is refracted from vacuum into a medium of refractive index 1.5, the wavelength of refracted light will be ​​
    

1. 1. dependent on intensity of refracted light

   
   
   

   2. same

   
   
   

   3. smaller

   
   
   

   4. larger

   
   
   

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1. View Hint View Answer Discuss in Forum

   From μ =	c	=	n λv	, λm =	λv
   	v		n λm		μ

   
   Here, c = velocity of light in medium and v = velocity of light in vacuum; ​
   µ = refractive index of the medium. ​
   Hence, wavelength in medium (λ_m) < λ_a
   (∵ µ > 1, given) ​
   So, the required wavelength decreases.
   ALTERNATIVELY, ​
   c = vλ . On refraction, the frequency, do not change. When light is refracted from vacuum to a medium, the velocity, c decreases. Therefore , λ also decreases.
   

   Correct Option: C

   From μ =	c	=	n λv	, λm =	λv
   	v		n λm		μ

   
   Here, c = velocity of light in medium and v = velocity of light in vacuum; ​
   µ = refractive index of the medium. ​
   Hence, wavelength in medium (λ_m) < λ_a
   (∵ µ > 1, given) ​
   So, the required wavelength decreases.
   ALTERNATIVELY, ​
   c = vλ . On refraction, the frequency, do not change. When light is refracted from vacuum to a medium, the velocity, c decreases. Therefore , λ also decreases.
   

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19. A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices µ₁ and µ₂ and R is the  radius of curvature of the curved surface of the lenses, then the focal length of the combination is

1. 1. 	R
      	2(µ1 - µ2)

   
   
   

   2. 	R
      	(µ1 - µ2)

   
   
   

   3. 	2R
      	(µ2 - µ1)

   
   
   

   4. 	R
      	2(µ1 + µ2)

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   	1	=	1	+	1
   	f		f1		f2

   
   

   = (μ1 - 1)		1	-	1		+ (μ2 - 1)		1	-	1
   		∞		-R				∞		R

   
   

   =	(μ1 - 1)	-	(μ2 - 1)	⇒	1	=	μ1 - μ2
   	R		R		f		R

   
   

   ⇒ f =	R
   	μ1 - μ2

   
   

   Hence, focal length of the combination is	R
   	μ1 - μ2

   
   

   Correct Option: B

   
   

   	1	=	1	+	1
   	f		f1		f2

   
   

   = (μ1 - 1)		1	-	1		+ (μ2 - 1)		1	-	1
   		∞		-R				∞		R

   
   

   =	(μ1 - 1)	-	(μ2 - 1)	⇒	1	=	μ1 - μ2
   	R		R		f		R

   
   

   ⇒ f =	R
   	μ1 - μ2

   
   

   Hence, focal length of the combination is	R
   	μ1 - μ2

   
   

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20. When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index.​​​
    

1. 1. equal to that of glass

   
   
   

   2. less than one ​

   
   
   

   3. greater than that of glass

   
   
   

   4. less than that of glass

   
   
   

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1. View Hint View Answer Discuss in Forum

   1	=		μg	- 1				1	-	1
   f			μm					R1		R2

   
   

   If µg = µm, then	1	= (1 - 1)		1	-	1
   	f			R1		R2

   
   

   ⇒	1	= 0
   	f

   
   

   ⇒ f =	1	= ∞
   	0

   
   This implies that the liquid must have refractive index equal to glass.

   Correct Option: A

   1	=		μg	- 1				1	-	1
   f			μm					R1		R2

   
   

   If µg = µm, then	1	= (1 - 1)		1	-	1
   	f			R1		R2

   
   

   ⇒	1	= 0
   	f

   
   

   ⇒ f =	1	= ∞
   	0

   
   This implies that the liquid must have refractive index equal to glass.

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