Question

what is the minimum distance between an object and its real image formed by a concave mirror of focal length f?

Answer 1

Hello Dear.

Here is the answer---

The minimum distance between the object and its real image formed by the concave mirror is zero.

In such an Situation, Distance between the object and the image is always equal.

Also, In this case, distance between the object and the mirror is equal to twice the focal length.

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Although if the proper values are given, then it can also be calculated by the Formula which is proved below.

Let the Image distance and the object distance be v and u respectively.

Since the Image is real,
∴ Image Distance = v(negative)
Object Distance = u (negative)
Focal Length = f (negative)

Now,
Using the Lens Formula,

  $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
⇒ [tex] \frac{1}{-f} = \frac{1}{-v} + \frac{1}{-u}[/tex]
⇒ $\frac{1}{-f} = \frac{-u - v}{vu}$
⇒  vu = -f(- u - v)
⇒ vu = f( u + v)
⇒ vu = f (u + v)
⇒ u + v = vu/f


If the Proper given values are substituted in the formula, then the answer can be easily calculated.


Hope it helps.