Tag: derivation of formula for curved mirrors

Questions Related to derivation of formula for curved mirrors

An object is placed in front of a concave mirror of radius of curvature 15 cm, at a distance of 10 cm, the position and nature of the image formed is :

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $+30 cm, virtual \ and \ erect$

  2. $+30 cm, real \ and \ inverted$

  3. $-30 cm, virtual \ and \ erect$

  4. $-30 cm, real \ and \ inverted$

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Correct Option: D

An object of length $6\ cm$ is placed on the principle axis of a concave mirror of focal length $f$ at a distance of $4\ f$. The length of the image will be

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $2\ cm$

  2. $12\ cm$

  3. $4\ cm$

  4. $1.2\ cm$

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Correct Option: A
Explanation:

Given that,

The object distance $u=-6\,cm$

Now, magnification is

  $ m=\dfrac{I}{O} $

 $ m=\dfrac{f}{f-u} $

 $ \dfrac{I}{6}=\dfrac{-f}{-f-\left( -4f \right)} $

 $ I=-2\,cm $

Hence, the length of image is -$2\ cm$

An astronomical telescope has focal lengths $100$ & $10$cm of objective and eyepiece lens respectively when final image is formed at least distance of distinct vision,magnification power of telescope will be,

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. -15

  2. -14

  3. -17

  4. -19

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Correct Option: B
Explanation:

Given focal length of eye piece${f} _{e}=10cm\$

focal length of objective${f} _{o}=100 cm\$
Also we know least distance $D=25 cm\$ 
Magnifying power $M=\dfrac{-{f} _{0}}{{f} _{e}}(1+\dfrac{{f} _{e}}{D})\$
$M=-\dfrac{100}{10}(1+\dfrac{10}{25})\$
$M=-14$

In the displacement method, a convex lens is placed in between an object and a screen. If one of the magnification is $3$ and the displacement of the lens between the two positions is $24$cm, then the focal length of the lens is:

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $10$ cm

  2. $9$ cm

  3. $6$ cm

  4. $16/3$ cm

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Correct Option: B
Explanation:

Given magnification $M=\dfrac{v}{u}=3$


Thus $v=3u$, where v and u are the image and object distance respectively.

Also Distance between lenses$=v-u=24$
Thus $u=12 cm$, than $v=36 cm$

From lens formula we have,
$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$

$\dfrac{1}{f}=\dfrac{1}{36}+\dfrac{1}{12}$

$\dfrac{1}{f}=\dfrac{4}{36}$

$f=\dfrac{36}{4}$

$f=9 cm$

A concave mirror of focal length $20\ cm$ produces an image twice the height of the object. If the image is real, then the distance of the object from the mirror is:

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $20\ cm$

  2. $60\ cm$

  3. $10\ cm$

  4. $30\ cm$

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Correct Option: D

In a concave mirror an object is placed at a distance x from the focus, and the image is formed at a distance y from the focus. The focal length of the mirror is

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $xy$

  2. $\sqrt{xy} $

  3. $\dfrac{x+y}{2} $

  4. $\sqrt{\dfrac{x}{y} }$

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Correct Option: B

Sun subtends an angle of $0.5^{o}$ at the pole of a concave mirror of radius of curvature 15 m. The diameter of the image of the sun formed by the mirror is

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $8.55 cm$

  2. $7.55 cm$

  3. $6.55 cm$

  4. $5.55 cm$

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Correct Option: A

A light ray travelling parallel to the principle axis of a concave mirror strikes the minor at angle of incidence $\theta$. If the radius of curvature of the mirror is $R$, then after reflection, the ray meets the principle axis at distance $d$ from the centre of curvature, then $d$ is 

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $\dfrac {R}{2}$

  2. $R\left(1-\dfrac {1}{2\cos \theta}\right)$

  3. $\dfrac {R}{2\cos \theta}$

  4. $\dfrac {R}{2}(1+\cos \theta)$

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Correct Option: A

The focal length of a concave mirror is f and the distance from the object to the principal focus is p. The ratio of the size of the real image to the size of the object is:

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. $-\displaystyle \frac{f}{p}$

  2. $\displaystyle \left(\frac{f}{p}\right)^2$

  3. $\displaystyle \left(\frac{f}{p}\right)^{\frac{1}{2}}$

  4. $-\displaystyle \frac{p}{f}$

  5. $-fp$

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Correct Option: A
Explanation:

Distance of object is $u= -(f+p)$
$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$ gives:
$\dfrac{1}{v}-\dfrac{1}{f+p}= -\dfrac{1}{f}$
or, $\dfrac{1}{v}= -\dfrac{1}{f}+\dfrac{1}{f+p}$
or, $\dfrac{1}{v}= -\dfrac{p}{(f+p)\times f}$
or, $v= -\dfrac{(f+p)\times f}{p}$      (-ve sign indicates image is real) 
   Magnification $=-\dfrac{v}{u}$ 
           $=-\dfrac{(f+p)\times f}{p\times (f+p)}$   
           $=-\dfrac{f}{p}$  (-ve sign indicates inverted)
    So, ratio of size of image to that of object is: $-\dfrac{f}{p}$

A concave spherical mirror has a focal length of 12 cm. if an object is placed 6 cm in front of it, the position of the magic is 

physics reflection of light at curved surfaces problems on mirror and magnification formula derivation of formula for curved mirrors mirror formula and magnification

  1. 4 cm behind the mirror

  2. 4 cm in front of the mirror

  3. 12 cm behind the mirror

  4. 12 cm in front of the mirror

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Correct Option: A