41. The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length​
    

1. 1. 10 cm

   
   
   

   2. 15 cm

   
   
   

   3. ​20 cm

   
   
   

   4. 5 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   The silvered plano convex lens behaves as a concave mirror ; whose focal length is given by
   

   	1	=	2	+	1
   	F		f1		fm

   
   
   If plane surface is silvered
   

   fm =	R2	=	∞	= ∞
   	2		2

   
   

   ∴	1	= (μ - 1)		1	-	1
   	f1			R1		R2

   
   

   	= (μ - 1)		1	-	1		=	μ - 1
   			R		∞			R

   
   

   ∴	1	=	2(μ - 1)	+	1	=	2(μ - 1)
   	F		R		∞		R

   
   

   F =	R
   	2(μ - 1)

   
   Here, R = 10 cm, µ = 1.5
   

   ∴ F =	10	= 10 cm
   	2(1.5 - 1)

   Correct Option: A

   The silvered plano convex lens behaves as a concave mirror ; whose focal length is given by
   

   	1	=	2	+	1
   	F		f1		fm

   
   
   If plane surface is silvered
   

   fm =	R2	=	∞	= ∞
   	2		2

   
   

   ∴	1	= (μ - 1)		1	-	1
   	f1			R1		R2

   
   

   	= (μ - 1)		1	-	1		=	μ - 1
   			R		∞			R

   
   

   ∴	1	=	2(μ - 1)	+	1	=	2(μ - 1)
   	F		R		∞		R

   
   

   F =	R
   	2(μ - 1)

   
   Here, R = 10 cm, µ = 1.5
   

   ∴ F =	10	= 10 cm
   	2(1.5 - 1)

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42. A body is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance 'd' ahead of second wall, then the required focal length will be​

1. 1. only	d
      	4

   
   
   

   2. only	d
      	2

   
   
   

   3. more than	d	but less than	d
      	4		2

      ​

   
   
   

   4. ​less than	d
      	4

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using the lens formula ,	1	=	1	-	1
   	f		v		u

   
   Given v = d, for equal size image ​| v | = | u | = d
   By sign convention u = –d
   

   ∴	1	=	1	+	1	or f =	d
   	f		d		d		2

   
   

   Correct Option: B

   Using the lens formula ,	1	=	1	-	1
   	f		v		u

   
   Given v = d, for equal size image ​| v | = | u | = d
   By sign convention u = –d
   

   ∴	1	=	1	+	1	or f =	d
   	f		d		d		2

   
   

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43. A convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will​
    

1. 1. remain unchanged

   
   
   

   2. become zero

   
   
   

   3. become infinite

   
   
   

   4. become small, but non-zero

   
   
   

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1. View Hint View Answer Discuss in Forum

   1	= (ℓμg - 1)		1	-	1
   f			R1		R2

   
   where , _ℓμ_g = 1 is given
   

   ⇒	1	= (1 - 1)		1	-	1		= 0 ⇒ f = ∞
   	f			R1		R2

   Correct Option: C

   1	= (ℓμg - 1)		1	-	1
   f			R1		R2

   
   where , _ℓμ_g = 1 is given
   

   ⇒	1	= (1 - 1)		1	-	1		= 0 ⇒ f = ∞
   	f			R1		R2

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44. An equiconvex lens is cut into two halves along (i) XOX' and (ii) YOY' as shown in the figure. Let f, f ', f '' be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively.​​​
    
    Choose the correct statement from the following ​
    

1. 1. f ' = 2f, f '' = 2f ​

   
   
   

   2. f ' = f, f '' = 2f ​

   
   
   

   3. f ' = 2f, f '' = f ​

   
   
   

   4. f ' = f, f '' = f

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   	1	= (μ - 1)		1	-	1
   	f			R1		R2

   
   In this case, R₁ and R₂ are unchanged ​
   So, f will remain unchanged for both pieces of the lens
   ∴ f = f '​
   
   

   	1	=	1	+	1
   	f		f1		f2

   
   This is combination of two lenses of equal focal lengths
   

   ∴	1	=	1	+	1	=	2	⇒ f" = 2f
   	f		f"		f"		f"

   Correct Option: B

   
   

   	1	= (μ - 1)		1	-	1
   	f			R1		R2

   
   In this case, R₁ and R₂ are unchanged ​
   So, f will remain unchanged for both pieces of the lens
   ∴ f = f '​
   
   

   	1	=	1	+	1
   	f		f1		f2

   
   This is combination of two lenses of equal focal lengths
   

   ∴	1	=	1	+	1	=	2	⇒ f" = 2f
   	f		f"		f"		f"

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45. A convex  lens and a concave lens, each having same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is​
    

1. 1. 50

   
   
   

   2. infinite

   
   
   

   3. zero

   
   
   

   4. 25

   
   
   

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1. View Hint View Answer Discuss in Forum

   From the formula,
   

   	1	=	1	+	1	=	1	-	1	= 0
   	f		f1		f2		25		25

   
   

   Power of combination =	1	= 0
   	f

   Correct Option: C

   From the formula,
   

   	1	=	1	+	1	=	1	-	1	= 0
   	f		f1		f2		25		25

   
   

   Power of combination =	1	= 0
   	f

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