Question

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Answer 1

Given :

In a concave len,

Object height = 3cm

Object distance = - 10cm

focal length = - 15cm

Remember :- In concave mirror focal length is always negative

To find :

The size of the image

Solution :

Using lens formula that is,

The formula which gives the relationship between image distance, object distance and focal length of a lens is known as the lens formula.

The lens formula can be written as :

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

where,

• v denotes image distance
• u denotes object distance
• f denotes focal length

by substituting all the given values in the formula,

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

$\leadsto{ \sf \dfrac{1}{v} - \dfrac{1}{ - 10}= \dfrac{1}{ - 15}}$

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{10}= - \dfrac{1}{ 15}}$

$\leadsto{ \sf \dfrac{1}{v} = - \dfrac{1}{15} - \dfrac{1}{10}}$

$\leadsto{ \sf \dfrac{1}{v} = - \dfrac{1}{15} - \dfrac{1}{10}}$

$\leadsto{ \sf \dfrac{1}{v} = - \dfrac{ - 2 - 3}{30} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{ - 3}{30}}$

$\leadsto{ \sf \dfrac{1}{v} = - \dfrac{1}{10}}$

$\leadsto{ \sf v = - 10 \: cm}$

thus, image distance is -10cm.

Now, using magnification formula i.e.,

$\boxed{ \bf m = \dfrac{h'}{h} = \dfrac{v}{u}}$

here,

• m denotes magnification
• h' denotes image height
• h denotes object height
• u denotes object distance
• v denotes image distance

by substituting all the given values,

$\leadsto{ \sf \dfrac{h'}{h} = \dfrac{v}{u}}$

$\leadsto{ \sf \dfrac{h'}{3} = \dfrac{-10}{-10}}$

$\leadsto{ \sf {h'} = 3 \: cm}$

thus, the size of the image is 3 cm.

Answer 2

Answer:

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