Tag: ray optics and optical instruments

Quizzes (21) Questions (129)

Questions Related to ray optics and optical instruments

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

A convex lens has a focal length of $0.5 m$. It has to be combined with a second lens, so that the combination has a power of $1.5$ dioptre. Which of the following could be the second lens?

  1. A concave lens of focal length $2 m$
  2. Another convex lens of focal length $0.5 m$
  3. A concave lens of focal length $0.5 m$
  4. A convex lens of focal length $2 m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Power of combination $P = 1.5 $ dioptre

Power of convex lens having focal length of $0.5 m$,  $P _1 = \dfrac{1}{0.5}$ dioptre
Using $P = P _1 + P _2$
$\therefore$ $1.5 = \dfrac{1}{0.5} + P _2$
We get $P _2 = -0.5$ dioptre
Thus focal length of second lens $f _2 = \dfrac{1}{P _2}$ 
$\implies$ $f _2 =- \dfrac{1}{0.5} = -2 m$ (negative sign implies the lens must be a concave lens)
Thus second lens could be concave lens of focal length $2m$.

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

A combination of convex and concave lenses has power $ 4 D $ .If the convex lens has power $5 D $ focal length of the concave lense will be 

  1. $ 100 cm$
  2. $ -100 cm$
  3. $-1 cm$
  4. $-\dfrac{100}{9}cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Power of combination 
$P=P _1+P _2$
$\Rightarrow   4=5+P _2$
$\Rightarrow  P _2=4-5=-1 D$
$\therefore   -1=P _2=\dfrac{100}{f(cm)}$
$\therefore   f=-100 cm$

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

Two identitical thin plano-convex glass lenses (refractive index 1.5 ) each having radius of curvature of 20 cm are placed with their convex surface in contact at the centre .The intervening space is filled with oil of refractive index 1.7.The focal length of the combination is 

  1. -20 cm

  2. -25 cm

  3. -50 cm

  4. 50 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The intervening space will act as concave lens.

Thus, the net focal length of the combination of three lenses would be given as, $\dfrac{1}{f} = \dfrac{1}{f _1}+\dfrac{1}{f _2}+\dfrac{1}{f _3}$

Now by the lens makers' formula,
$\dfrac{1}{f _1}=(1.5-1)\bigg(\dfrac{1}{\infty}-\dfrac{1}{-20}\bigg)=\dfrac{1}{40}$
$\dfrac{1}{f _2}=(1.7-1)\bigg(\dfrac{1}{-20}-\dfrac{1}{20}\bigg)=-\dfrac{2.8}{40}$
$\dfrac{1}{f _3}=(1.5-1)\bigg(\dfrac{1}{20}-\dfrac{1}{\infty}\bigg)=\dfrac{1}{40}$
$\therefore \dfrac{1}{f}=-\dfrac{0.8}{40}\implies f=-50cm$

Option C is correct.

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

A lens of power $6D$ is put in contact with a lens of power $-4\ D$. The combination will behave like a:

  1. Divergent lens of focal length $25\ cm$
  2. Convergent lens of focal length $50\ cm$
  3. Divergent lens of focal length $20\ cm$
  4. Convergent lens of focal length $100\ cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a combination of lenses, net power of the combination is given by sum of individual powers i.e.

            Pnet = ${ P } _{ 1 }+{ P } _{ 2 }$
According to question
            Pnet = 6D - 4D = +2D
hence it will be convergent lens of focal length = $\dfrac { 100 }{ 2 } cm=50cm$

Multiple choice physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

A convex lens of 2 D power is joined with a concave mirror of 1 D power. Equivalent power of instrument will be

  1. $-3D$
  2. $+3D$
  3. $-5D$
  4. $+5D$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The power of a lens is P = 1/f. When a lens and a mirror are combined, the equivalent power is P_eq = P_lens + P_mirror. Given P_lens = +2D and P_mirror = +1D, the total power is +3D.

Multiple choice physics ray optics and optical instruments problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

If image is real and inverted, mangification will be:

  1. two

  2. negative

  3. one

  4. zero
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to new Cartesian sign convention, image size for erect image is considered positive and that of inverted image is considered negative.

The object being always erect, the object size is always positive.
So, magnification for a real image, being a ratio of image size and object size is considered negative.