Question

A convex lens of focal length 30cm produces 5 times magnified real image of an object. What is the object distance?
(A) 36cm
(B) 25cm
(C) 30cm
(D) 150cm

Answer 1

Hint- The relationship between the image distance, object distance and the focal length of the lens is given by the Lens law. Lens law plays an important role in the field of optics.
Formula used: To solve this type of question we use the following formula.
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$
This is the lens formula. Where f is focal length of the lens, v is image distance and u is object distance.
$m = \dfrac{v}{u}$
This is the formula for magnification. If the image is real then magnification is negative and if virtual then magnification is positive.
Complete step by step answer:
In the question following values are given, f = 30cm, m= 5.
We have to find object distance (u).
Now because the image is real therefore magnification will be negative.
$m = - \dfrac{v}{u}$
Let us substitute the values in the above equation.
$5 = - \dfrac{v}{u}$
Now we can write the value of v in terms of u.
$v = - 5u$ (1)
Now let us use the formula $\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$ and substitute the values.
$\dfrac{1}{{30}} = \dfrac{1}{{ - 5u}} - \dfrac{1}{u}$
Now, let us further simplify it.
$\dfrac{1}{{30}} = - \dfrac{6}{{5u}} \Rightarrow 5u = - 180$
So, we get the following value of u.
$u = - 36cm$
Hence, option (A) $36cm$ is the correct option.

Additional information:
Magnification is the increase or decrease in the size of the image of an object produced by the lens as compared to its true size.
There are two types of magnification, linear and angular magnification. But the commonly encountered is linear magnification.
Magnification refers to change in apparent size not the physical size of the object.

Note: By knowing the value of magnification only we can predict the type of image formed.
If magnification is a negative value then the image formed will be the real image and for negative magnification the image formed will be virtual.