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Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

The suns diameter is $1.4\times { 10 }^{ 9 }m$ and its distance from the earth is ${ 10 }^{ 11 }m$. The diameter of its image, formed by a convex mirror of focal length 2m will

  1. 0.7 cm

  2. 1.4 cm

  3. 2.8 cm

  4. 10 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a mirror, the magnification m = -v/u = f/(f-u). Given the sun is very far away (u is large), the image is formed at the focus f. The size of the image is h_i = h_o * (f/u). Plugging in values: (1.4 * 10^9) * (2 / 10^11) = 2.8 * 10^-2 m = 2.8 cm.

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

The distance of real object when a concave mirror produces a real image of magnification $'m'$ is ($f$ is focal length)

  1. $\left(\frac{m - 1}{m}\right) f$
  2. $\left(\frac{m + 1}{m}\right) f$
  3. $(m-1)f$
  4. $(m+1)f$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a concave mirror, magnification m = f / (f - u). Rearranging for u: m(f - u) = f, mf - mu = f, mu = mf - f, u = f(m - 1) / m. However, for a real image, m is negative. Using m = -|m|, the distance u = f(1 + |m|) / |m|.

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

Converging rays are incident on a convex spherical mirror so that their extensions intersect  $30 cm$  behind the mirror on the optical axis. The reflected rays form a diverging beam, so that their extensions intersect the optical axis  $1.2 m$  from the mirror. The focal length of the mirror is

  1. $40{ cm }$
  2. $60{ cm }$
  3. $30{ cm }$
  4. $24{ cm }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the mirror formula 1/v + 1/u = 1/f. For converging rays, u = +30 cm (virtual object). The reflected rays form a diverging beam with image at v = -120 cm. 1/(-120) + 1/30 = 1/f. 1/f = (-1 + 4) / 120 = 3/120 = 1/40. So f = 40 cm.

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

Magnification produced by a rear view mirror fitted in vehicles

  1. is less than one

  2. is more than one

  3. is equal to one

  4. can be more than or less than one depending upon the position of the object in front of it.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rear view mirrors in vehicles are convex mirrors. They are designed to provide a wider field of view by forming diminished images, so the magnification is always less than one.

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

A concave mirror of radius of curvature 40 cm forms an image of an object placed on the principal axis at a distance 45 cm in front of it. Now if the system (including object) is completely immersed in water $(\mu=1.33)$, then:

  1. the image will shift towards the mirror.

  2. the magnification will reduce.

  3. the image will shift away from the mirror and magnification will increase.

  4. the position of the image and magnification will not change.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mirror operates on the principle of Laws of reflection. 

Therefore, focal length does not depend upon the medium and object distance is also unchanged, so their will be no change in the image distance, correspondingly magnification will also remain unchanged.

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

The distance at which an object should be placed in front of a convex lens of focal length 10 cm to obtain a real image double the size of object will be:

  1. 30 cm

  2. 15 cm

  3. 5 cm

  4. 10 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Convex lens gives the real and double-sized image when the object is placed exactly between the focus and radius of curvature.
We have, $\displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$m = \displaystyle \frac{v}{u} = 2$ or $v = 2u$


$\therefore \displaystyle \frac{1}{f} = \frac{1}{2u} - \frac{1}{-u} = \frac{1}{2u} + \frac{1}{u} = \frac{3}{2u}$

or $\displaystyle \frac{1}{10} = \frac{3}{2u}$ or $u = 15 cm$

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

An object is placed at the centre of curvature of a concave mirror of radius of curvature $20$cm. The nature and position of the image shall be.

  1. Virtual and $15$cm from the mirror
  2. Real and $20$cm from the mirror
  3. Virtual and $20$cm from the mirror
  4. Real and $10$cm from the mirror
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Image of an object placed at center of curvature is inverted, real and of the same size and is formed at the center of curvature. Hence image will be real and at the center of curvature (20 cm from mirror).

Multiple choice physics reflection of light in spherical mirrors focus and focal length spherical mirror formula and magnification reflection of light by curved surfaces

Formula of focal length in convex lens is

  1. $\displaystyle f = \frac{u+v}{u-v}$
  2. $\displaystyle f = \frac{u\times v}{u-v}$
  3. $\displaystyle f = \frac{u-v}{u+v}$
  4. $\displaystyle f = \frac{u+v}{u+v}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The standard lens formula is 1/v - 1/u = 1/f. Solving for f gives f = (uv) / (u - v).