46. A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the Sun is 1.39 ×10⁹ m and its mean distance from the earth is 1.5 × 10¹¹ m. What is the diameter of the Sun’s image on the paper?​​
    

1. 1. 9.2 × 10^–4 m

   
   
   

   2. 6.5 × 10^–4 m

   
   
   

   3. 6.5 × 10^–5 m

   
   
   

   4. 12.4 × 10^–4 m

   
   
   

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1. View Hint View Answer Discuss in Forum

   We have ,		v		=	Size of image
   		u			Size of object

   
   

   or , Size of image =		v		× Size of object
   		u

   
   

   =		10-1		× (1.39 × 109)
   		1.5 × 1011

   
   = 0.92 ×10^–3 m = 9.2 × 10^–4 m
   ∴ Diameter of the sun’s image  = 9.2 × 10^–4 m.
   

   Correct Option: A

   We have ,		v		=	Size of image
   		u			Size of object

   
   

   or , Size of image =		v		× Size of object
   		u

   
   

   =		10-1		× (1.39 × 109)
   		1.5 × 1011

   
   = 0.92 ×10^–3 m = 9.2 × 10^–4 m
   ∴ Diameter of the sun’s image  = 9.2 × 10^–4 m.
   

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47. Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is :​​​

1. 1. 		f1
      		f2

   
   
   

   2. 		f2
      		f1

   
   
   

   3. 	f1 + f2
      	2

   
   
   

   4. 	f1 + f2
      	f1 f2

   
   
   

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1. View Hint View Answer Discuss in Forum

   The focal length of the combination	1	=	1	+	1
   	f		f1		f2

   
   

   ∴ Power of the combinations, P =	f1 + f2		∴ P =	1
   	f1 f2			f

   Correct Option: D

   The focal length of the combination	1	=	1	+	1
   	f		f1		f2

   
   

   ∴ Power of the combinations, P =	f1 + f2		∴ P =	1
   	f1 f2			f

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48. A lens having focal length f and aperture of diameter d forms  an image of intensity I.Aperture

    of diameter	d	in central region of lens is covered by a black paper. Focal length of lens and
    	2

    
    intensity of image now will be respectively :

1. 1. f and	I
      	4

   
   
   

   2. 3f	and	I
      4		2

   
   
   

   3. f and	3I
      	4

   
   
   

   4. f	and	I
      2		2

   
   
   

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1. View Hint View Answer Discuss in Forum

   By covering aperture, focal length does not change. But intensity is reduced by	I
   	4

   
   

   times, as aperture diameter	d	is covered.
   	2

   
   

   ∴ I' = I -	I	=	3I
   	4		4

   
   

   ∴ ​​New focal length = f and intensity =	3I	.
   	4

   Correct Option: C

   By covering aperture, focal length does not change. But intensity is reduced by	I
   	4

   
   

   times, as aperture diameter	d	is covered.
   	2

   
   

   ∴ I' = I -	I	=	3I
   	4		4

   
   

   ∴ ​​New focal length = f and intensity =	3I	.
   	4

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49. A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is​​​​
    

1. 1. – 10 cm

   
   
   

   2. 20 cm

   
   
   

   3. –30 cm

   
   
   

   4. 5 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   By lens formula,
   

   	1	-	1	=	1
   	v		u		f

   
   u = 10 cm ​
   v = 15 cm ​
   f = ? ​
   Putting the values, we get
   

   	1	-	1	=	1
   	15		10		f

   
   

   	10 - 15	=	1
   	150		f

   
   

   ∴ f = -	150	= -30 cm
   	3

   
   

   Correct Option: C

   
   By lens formula,
   

   	1	-	1	=	1
   	v		u		f

   
   u = 10 cm ​
   v = 15 cm ​
   f = ? ​
   Putting the values, we get
   

   	1	-	1	=	1
   	15		10		f

   
   

   	10 - 15	=	1
   	150		f

   
   

   ∴ f = -	150	= -30 cm
   	3

   
   

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