Question

An converging mirror of focal length 20cm forms an image which is twice the size of the object.calculate two possible distances of the object from the mirror?

Answer 1

hello friend..!!

according to the given question , we know that the mirror formula is 

1/f = 1/v + 1/u ---------(1)

where f → focal length = -20 cm
v → image distance 
u→object distance 

now, according to the given question ,

hi / ho = - V/U = 2 

⇒ hi = 2ho also v = -2u 

since we got v = -2u -----(2)

now by substituting equation (2) in (1) gives 

⇒ -1/20 = -1/2u + 1/u

⇒ -1/20 = -1 + 2 / 2u

⇒ -1/20 = 1/2u 

⇒ 2u = - 20 

⇒ u = -10 cm 

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hope it is useful...!!

Answer 2

Answer:

Concept:

The reflecting surface of a concave mirror, also known as a converging mirror, bulges forward (away from the incident light). Light is reflected inward by concave mirrors to a single focus point. They're utilized to concentrate light. A mirror with a curved reflecting surface is known as a curved mirror. Convex or concave surfaces are possible. The surfaces of most curved mirrors are formed like a section of a sphere, however alternative shapes are occasionally utilized in optical equipment.

Given:

An converging mirror of focal length 20cm forms an image which is twice the size of the object.

Find:

calculate two possible distances of the object from the mirror?

Answer:

Given that,

$f = - 20 cm \\h1 = 2h0$

where,

$h1$ stands for image height, and

$h0$ stands for object height

Now, $m = -v /u$

             $= h1/h0\\= -v/u\\= 2h0/h0\\= -v/u =2$

      $= v = -2u -----(1)$

Using the mirror formula, we were able to

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

$\frac{1}{-20} =\frac{1}{u} -\frac{1}{2u}$ (∴ $v=-2u$)

$\frac{1}{-20} =\frac{1}{2u}$

both sides while taking reciprocals

$-20 = 2u\\-10 = u$

Using this value equation -----> 1

$v = - (-20)\\v = 20$

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