Tag: reflection of light at curved surfaces

Questions Related to reflection of light at curved surfaces

If magnification is positive, the nature of the image 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. real and inverted

  2. virtual and erect

  3. real

  4. none of these

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Correct Option: B
Explanation:

$\text{Magnification}=\dfrac{\text{Image  size}}{\text{Object  size}}$

According to new Cartesian sign convention, size of height of real and inverted image is considered negative and that of virtual and erect image is considered positive.
The heigh of the object, being erect is considered positive always.
So, for positive magnification, the ratio, mentioned above, will be positive. This implies that the image height will also be positive.
The image will be virtual and erect.

A concave mirror is made from a hollow sphere of radius of curvature 30 cm.  If an object of height 2 cm is placed at 10 cm from the pole of the mirror, determine the size of the image :

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

  1. 3 cm

  2. 6 cm

  3. 12 cm

  4. 24 cm

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Correct Option: B
Explanation:

Given: $u=-10cm$


$f=-15cm$

$h _{o}=2cm$

To find, $h _{o}$

From mirror formula,

$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$

$\dfrac{1}{v}-\dfrac{1}{10}=-\dfrac{1}{15}$

$\dfrac{1}{v}=\dfrac{1}{10}-\dfrac{1}{15}=\dfrac{5}{150}$

$v=30cm$

$magnification=\dfrac{h _{i}}{h _{o}}=\dfrac{-v}{u}$

$\dfrac{h _{i}}{2}=\dfrac{-30}{-10}$

$h _{i}=6cm$

An object is placed on the principal axis of a concave mirror at a distance of 60 cm.  If the focal length of the concave mirror is 40 cm then determine the magnification of the obtained image.

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

  2. -2

  3. -4

  4. +2

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Correct Option: B
Explanation:

Given: $u=-60 cm$     $f=-40 cm$
To find : $m$
Solution: From mirror formula
$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}$
$\dfrac{1}{v}-\dfrac{1}{60}=\dfrac{-1}{40}$
$\dfrac{1}{v}=\dfrac{1}{60}-\dfrac{1}{40}$
$v=-120 cm$
Hence magnification is given by
$m=\dfrac{-v}{u}=-\dfrac{(-120)}{(-60)}$
$m=-2$

Calculate the magnification of an object if it is kept at a distance of $3 cm$ from a concave mirror of focal length $4 cm$:

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

  1. $3$

  2. $6$

  3. $9$

  4. $4$

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Correct Option: D
Explanation:

$\dfrac{1}{u}+\dfrac{1}{v}=\dfrac{1}{f}$

$\dfrac{1}{-3}+\dfrac{1}{v}=\dfrac{1}{-4}$
$\dfrac{1}{v}=\dfrac{1}{12}$
v= 12 cm
Magnification
$=\dfrac{12}{3}=4$

A concave mirror produces $2$ times magnified real image of an object placed at $5 cm$ in front of it. Where is image located?

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. $-5 cm$

  3. $-10 cm$

  4. $2.5 cm$

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Correct Option: C
Explanation:

Magnification, $m = \dfrac {-v}{u}$
Given, magnification, $m = -2$

$-2 = \dfrac {-v}{-5 cm}$
Therefore, object distance, $v = -2\times 5 cm = -10 cm$

Magnification produced by plane mirror is $+1$. It means:

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

  1. Image formed by plane mirror is greater than size of the object

  2. Image formed by plane mirror is erect and of same size as the object

  3. Image formed by plane mirror is smaller than size of object and is virtual

  4. None

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Correct Option: B
Explanation:

Magnification $= +1$ signifies that the image formed in a plane mirror is of same size as the object. Positive sign in the value of magnification signifies that image formed by a plane mirror is erect.

The radius of curvature of concave mirror is 24 cm and the image is magnified by 1.5 times. The object distance 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. 8 cm

  3. 16 cm

  4. 24 cm

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Correct Option: A
Explanation:

Given that, $\displaystyle R=-24$cm
$\displaystyle f=-12cm$ and $\displaystyle m=1.5$
By the lens formula,
$\displaystyle \frac { 1 }{ v } +\frac { 1 }{ u } =\frac { 1 }{ f } $
$\displaystyle \frac { 1 }{ 1.5u } +\frac { 1 }{ u } =-\frac { 1 }{ 12 } $
$\displaystyle \frac { 2.5 }{ 1.5u } =-\frac { 1 }{ 12 } $
or, $\displaystyle u=-20cm$

We want a mirror that will make an object look larger. What combination of image and object distances (from the mirror) will accomplish this?

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

  1. Image Distance $3.0 cm$, Object Distance $3.0 cm$

  2. Image Distance $2.0 cm$, Object Distance $3.0 cm$

  3. Image Distance $3.0 cm$, Object Distance $5.0 cm$

  4. Image Distance $3.0 cm$, Object Distance $2.0 cm$

  5. Image Distance $3.0 cm$, Object Distance $10.0 cm$

Show answer
Correct Option: D
Explanation:

Magnification by a mirror         $m = \dfrac{-v}{u}$


For option D :    $m = \dfrac{- 3.0}{-2.0} = 1.5$             $\implies m>1$
Thus the data given in option D will make a larger image.

The magnification produced by a mirror is $+\dfrac{1}{3}.$ Then the mirror is a ____________.

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

  1. Concave mirror

  2. Convex mirror

  3. Plane mirror

  4. plano convex mirror

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Correct Option: B
Explanation:

The image produced is virtual and erect and also diminished.


Hence, the mirror must be $convex$ mirror. Concave mirror also produces virtual image but it is enlarged.But convex mirror always produces diminished virtual image.

Answer-(B)

In an experiment to determine the focal length ($f$) of a concave mirror by the $u-v$ method, a student places the object pin A on the principal axis at a distance $x$ from the pole $P$. The student looks at the pin and its inverted image from a distance keeping the eye in line with $PA$. When the student shifts the eye towards left, the image appears to the right of the object pin. Then:

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

  1. $x< f$

  2. $f< x< 2f$

  3. $x= 2f$

  4. $x> 2f$

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Correct Option: B
Explanation:

Since the object and the image move in opposite directions, the position of the object should be in between $f$ and $2f$.
So, $f < x < 2f$