Question

What is the minimum distance between an object and its real image, formed by a concave mirror? (b) State the laws of reflection​

Answer 1

Answer:

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Answer 2

Answer:

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Look at the figure. Here, O is point like object and I is it’s image.

u= object distance.

v= image distance.

f= focal length of the lens.

x= distance between object and image.

We have to find the minimum value of x for which we can get the real image.

We know that for a real image we will have to have v positive.

The only weapon with us is the formula for a thin lens:

1v−1u=1f ………………(1)

Now, from the figure, u=x−v . We substitute this value of u in equation (1), with remembering that according to Cartesian system of sign convention u is negative, we get

1v+1(x−v)=1f . Therefore,

(x−v+v)[v(x−v)]=1f . Therefore,

xf(vx−v2)=1

Or

xf=vx−v2 . Then,

v2−vx+xf=0 ……………….(2).

We have to consider the condition for the real root of this quadratic equation in v .

Now, the roots are

v=x±x2–4xf√2 .

For v to be real, x2≥4xf

OR x≥4f ……………(3).

Thus, for a real image by converging lens the minimum distance between object and image should be 4f , where f is the focal length of the lens.

hope it may help you.