Question

An object 10cm in height is placed at a distance of 36cm from a concave mirror. The image
is formed 18cm in front of the mirror. Find the height of the image.

Answer 1

Step-by-step explanation:

sumof−48and−58is=−106

=102−(−106)

=102+106

=208Substract the sum of -42 and -147 from the difference of -283 and -413

Answer 2

Given :

• We have been given an object with a height of 10 cm
• When it is placed in front of a Concave Mirror , at a Distance of 36 cm from it
• Image is formed at 18 cm

To Find :

• We have to find the height of Image

Concept Used :

Magnification is the ratio of Height of Image produced to the Height of object

Mathematically , it can be written as

$\large{\boxed{\sf{ m = \dfrac{H_i}{H_o}}}}$

Where the variables stand for

• $\sf{H_i}$ = Height of Image
• $\sf{H_o}$ = Height of Object

There is one more way to write the formula in terms of Object and Image Distance

$\large{\boxed{\sf{ m = - \dfrac{v}{u}}}}$

Solution :

Using proper sign convention in the given Question , we have been given that

• Object Distance (u) = - 36 cm
• Image Distance (v) = - 18 cm
• Height of Object = 10 cm

Equating both formulas of Magnification

$\longrightarrow \boxed{\sf{\dfrac{H_i}{H_o} = - \dfrac{v}{u}}}$

$\longrightarrow \sf{ H_i = -\dfrac{v}{u} \times H_o}$

Putting the values of all the given variables in the above Equation

$\longrightarrow \sf{ H_i = -\dfrac{(-18)}{-36} \times 10}$

$\longrightarrow \sf{ H_i = -\dfrac{\cancel{18}}{\cancel{36}} \times 10}$

$\longrightarrow \sf{ H_i = -\dfrac{1}{2} \times 10}$

$\longrightarrow \sf{ H_i = -\dfrac{10}{2} \times 10}$

$\longrightarrow \underline{\boxed{\sf{ H_i = - 5 \: cm}}}$

Hence Height of Image is 5 cm, minus sign here indicates that the image is real and inverted

$\underline{\boxed{\sf{\blue{Height \: of \: Image = 5 \: cm}}}}$

Properties of Image :

• Image formed is real and inverted
• Image is formed Diminished

$\large{\gray{\underline{\underline{\sf{Extra \: Information:}}}}}$

• A Concave Mirror is also known as Converging Mirror
• It converges all the right rays falling on its surface at a point know as focus
• Imagine formed can be real or virtual
• Image formed me enlarge or Diminished