Tag: thin lens

Quizzes (0) Questions (58)

Questions Related to thin lens

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

A point object is placed at a distance of $15 cm$ from a convex lens. The image is formed on the other side at a distance of $30cm$ from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by $30 cm$. Calculate the focal lengths of the concave and convex lenses.

  1. $10 cm, 60 cm$
  2. $ 20 cm, 30 cm$
  3. $60 cm, 10 cm$
  4. $30 cm, 20 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the convex lens, 1/v - 1/u = 1/f. 1/30 - 1/-15 = 1/f1 => 1/30 + 2/30 = 3/30 = 1/10, so f1 = 10 cm. With the concave lens, the image shifts by 30 cm, so the new image distance is 60 cm. 1/60 - 1/-15 = 1/F_eq => 1/60 + 4/60 = 5/60 = 1/12, so F_eq = 12 cm. Since 1/F_eq = 1/f1 + 1/f2, 1/12 = 1/10 + 1/f2 => 1/f2 = 1/12 - 1/10 = (5-6)/60 = -1/60. So f2 = -60 cm. The focal lengths are 10 cm and -60 cm.

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

Two lenses  of power  6 D and -2D are combined  to form a single lens.  The focal length of  this  lens will be 

  1. $\frac{3}{2}m$
  2. $\frac{1}{4}m$

  3. 4 m
  4. $\frac{1}{8}m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total power of a combination of lenses in contact is the algebraic sum of their individual powers, so P = 6 D + (-2 D) = 4 D. The focal length is the reciprocal of the power in meters, so f = 1/4 m.

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 $20cm$.