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Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

Two plano-convex lenses of glass of refractive index $1.5$ have radii of curvature $20\ cm$ and $30\ cm$. They are placed in contact with curved surfaces towards each other and the space between them is filled with a liquid of refractive index $4/3$. The focal length of the combination is

  1. $48\ cm$
  2. $72\ cm$
  3. $12\ cm$
  4. $28\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The system consists of two plano-convex lenses and a liquid lens. P_total = P1 + P2 + P_liquid. P1 = (1.5-1)/0.2 = 2.5D. P2 = (1.5-1)/0.3 = 1.67D. P_liquid = -2*(n_liq-1)/R_avg? No, the liquid lens is biconcave with radii 20 and 30. P_liq = (4/3 - 1) * (-1/20 - 1/30) = (1/3) * (-5/60) = -5/180 = -1/36. P_total = 1/40 + 1/60 - 1/36 = (9+6-10)/360 = 5/360 = 1/72. So f = 72 cm.

Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths?

  1. -15, 10

  2. -10, 15

  3. 75, 50

  4. -75, 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let focal length of convex lens be $f$


Then focal length of the concave lens $ =  - 1.5f$


Equivalent focal length $ =  \dfrac{- 1.5 f \times f }{ (-0.5f) }= 3f$
 
=>$ f = 10 cm$

So individual focal lengths are 10 cm and -15 cm

Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

A convex lens of focal length $f _1$ and a concave lens of focal length $f _2$ are placed in contact. The focal length of the combination is

  1. $(f _1 + f _2)$
  2. $(f _1 - f _2)$
  3. $\displaystyle \frac{f _1 f _2}{f _2 - f _1}$
  4. $\displaystyle \frac{f _1 f _2}{f _2 + f _1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \frac{1}{f} = \frac{1}{f _1}+ \frac{1}{- f _2} = \frac{f _2 - f _1}{f _1 f _2} ;        f = \frac{f _1f _2}{f _2 - f _1}$

Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

A lens of power +2 diopter is placed in contact with a lens of power -1 diopter. The combination will behave like

  1. a convergent lens of focal length 50 cm

  2. a divergent lens of focal length 100 cm

  3. a convergent lens of focal length 100 cm

  4. a convergent lens of focal length 200 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$P = P _1 + P _2 = + 2 - 1 = +1$ diopter, lens behaves as convergent
$F = \displaystyle \frac{1}{P} = \frac{1}{1} = 1m = 100 cm$

Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

The radius of curvature of the convex surface of a plano-convex lens is $10 cm$. What is the focal length of the plano-convex lens? (Here $\displaystyle \mu $ = $1.5$) 

  1. $10 cm$
  2. $20 cm$
  3. $15 cm$
  4. $5 cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\mu=1.5 , R _1=10cm , R _2=0$


As focal length is given by $\dfrac{1}{f}=(\mu-1)(\dfrac{1}{R _1}-\dfrac{1}{R _2})$  (lens maker formula)

$\dfrac{1}{f}=0.5\times (\dfrac{1}{10}-0)$

$f=20cm$

hence, the focal length of the plano-convex lens is $20cm$.

Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

Two thin lenses of focal lengths 20 cm and 25 cm are placed in contact. The effective power of the combination is :

  1. $\displaystyle \frac{1}{9}$ diopters

  2. 45 diopters

  3. 6 diopters

  4. 9 diopters
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$f _1=20cm=0.2m ; f _2=25cm=0.25m$
as power of lens is given by,
$P=\frac{1}{f}$
$P _1=\frac{1}{f _1}=\frac{1}{0.2}=5D$,
$P _2=\frac{1}{f _2}=\frac{1}{0.25}=4D$
so,The effective power of the combination is $5D+4D=9D$.
hence,option D is correct.

Multiple choice physics ray optics and optical instruments power of the lens thin lens combination of lenses

The power of a diverging lens is 10D and that of a converging lens is 6D. When these two lenses are placed in contact with each other. The power of their combination will be

  1. +16D

  2. -16D

  3. -4D

  4. +4D
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The focal length of diverging lens is
${ F } _{ 1 }=\dfrac { 1 }{ P } =-\dfrac { 1 }{ 10 }$
The focal length of converging lens is
${ F } _{ 2 }=\dfrac { 1 }{ P } =+\dfrac { 1 }{ 6 }  $
The focal length of combined lens is
$\dfrac { 1 }{ f } =\dfrac { 1 }{ { f } _{ 1 } } +\dfrac { 1 }{ { f } _{ 2 } } $

$P=\dfrac { 1 }{ f } =-10+6=-4D$
The combined lens will act as diverging (concave ) lens.
Option C is correct.