Question

7. A student is performing an experiment in which he wants to obtain a real
image twice the size of the object with a convex lens of focal length 15 cm.
At what distance should he place the object?
(a) More than 15 cm but less than 30 cm.
(b) More than 5 cm but less than 10 cm.
(c) More than 10 cm but less than 15 cm.
(d) More than 30 cm but less than 60 cm.​

Answer 1

Answer:

(a)More than 15cm but less than 30cm.

Answer 2

The distance of the object is more than 5 cm but less than 10 cm.

(b) is correct option.

Explanation:

Given that,

Focal length = 15 cm

Size of image = twice of size of object

We need to calculate the magnification

Using formula of magnification

$m=\dfrac{h'}{h}$

$m=\dfrac{2h}{h}$

$m=2$

We need to calculate the image distance

Using formula of magnification

$m=\dfrac{v}{u}$

Put the value into the formula

$2=\dfrac{v}{u}$

$v=2u$

We need to calculate the object distance

Using formula of lens

$\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{15}=\dfrac{1}{2u}-\dfrac{1}{u}$

$\dfrac{1}{15}=-\dfrac{1}{2u}$

$u=-7.5\ cm$

Negative sign shows the potion of the object in front of the lens.

So, the distance of the object is 7.5 cm.

Hence, The distance of the object is more than 5 cm but less than 10 cm.

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Topic : optics

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