Question

Calculate the distance of an object of height h from a concave mirror of focal length 10cm, so as to obtain a real image of magnification 2.

Answer 1

Let u be the object distance and v be the image distance and the magnification of the mirror be represented by m.

We know, f is the focal length.

Given,

height of object = h  

focal length , f = 10 cm.

m = - 2 (concave mirror)

mirror = concave  

-2 = -$\frac{v}{u}$

v = 2 u  

By the Mirror formula,

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

$\frac{1}{2u} +\frac{1}{u} = \frac{-1}{10}$

On solving, $2 u = -30$

$u = -15 cm$

Thus the object should be placed at 15 cm in front of mirror.

Answer 2

$\huge\boxed{Answer:-}$

$(u = -h) \: is \: the \: distance$

$(-10 cm = focal \: length) \\ </p><p>(-2= \frac{ - v}{x} = mirror) \\ </p><p>(-2h = v)$

mirror = - 2

Using Mirror formula:

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

$= \frac{1}{ - 2h} + \frac{1}{ - h} = \frac{1}{ - 10}$

Therefore, height from the concave mirror =15cm

Here,

• F = focal length
• X = Distance of Object
• V = The Distance of Image