Tag: ray optics and optical instruments

Questions Related to ray optics and optical instruments

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?

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

  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 $2 m$

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Correct Option: A
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 $2m$.

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 

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

  1. $ 100 cm$

  2. $ -100 cm$

  3. $-1 cm$

  4. $-\dfrac{100}{9}cm$

Show answer
Correct Option: B
Explanation:

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

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 

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

  1. -20 cm

  2. -25 cm

  3. -50 cm

  4. 50 cm

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Correct Option: C
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.

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

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

  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 $100\ cm$

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Correct Option: B
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 = $\dfrac { 100 }{ 2 } cm=50cm$

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

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

  1. $-3D$

  2. $+3D$

  3. $-5D$

  4. $+5D$

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Correct Option: B

If image is real and inverted, mangification will be:

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

  1. two

  2. negative

  3. one

  4. zero

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Correct Option: B
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.

The magnification produced by a concave mirror

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

  1. is always more than one

  2. is always less than one

  3. is always equal to one

  4. may be less than or greater than one

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Correct Option: D
Explanation:

if object distance < f then m>1

else if object distance >f then m<1

The mirror used in automobiles to see the rear field of view is

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

  1. concave

  2. convex

  3. plane

  4. none of these

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Correct Option: B
Explanation:

Convex mirrors are used in automobiles to see the near field of view as convex mirror has a wider field of view and it has higher magnification.