Question

11, A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.​

Answer 1

$\red{\huge{Answer}}$

$\boxed{-30 \: cm}$

Focal length, f = -15 cm

Image distance, v = -10 cm

Object distance, u = ?

We know lens formula,

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

$\frac{1}{ - 15} \: = \frac{1}{ - 10} \: - \frac{1}{u} \\ \\ \frac{ - u - 10}{10u} = \frac{ - 1}{15} \\ \\ - 15u \: - 150 \: = \: - 10u \\ \\ - 5u = \: 150 \\ \\ u = - 30$

Hence, distance of object from mirror is 30 cm.

[Note:- Negative sign (-) denotes that the object is in front of the mirror.]

Answer 2

AnsweR:

Given:

• Focal length = -15 cm
• Image distance = -10 cm

To Find:

• Object distance
• Ray diagram

Solution:

We know that,

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

Putting the values given,

$\mapsto\tt{\dfrac{1}{-15}=\dfrac{1}{-10}-\dfrac{1}{u}}$

$\mapsto\tt{\dfrac{-1}{u}=\dfrac{1}{-15}-\dfrac{1}{-10}}$

$\mapsto\tt{\dfrac{-1}{u}=\dfrac{1}{-15}+\dfrac{1}{10}}$

$\mapsto\tt{\dfrac{-1}{u}=\dfrac{10-15}{-150}}$

$\mapsto\tt{\dfrac{-1}{u}=\cancel{\dfrac{-5}{-150}}}$

$\mapsto\tt{\dfrac{-1}{u}=\dfrac{1}{30}}$

$\mapsto{\green{\tt{u=-30\:cm}}}$

So, the object distance = 30 cm.

Refer to the day diagram in the image attached.

$\rule{200}4$