Question

Describe the nature of the image formed when the object is placed at a distance of 20cm from a concave mirror of focal length 10cm​

Answer 1

Answer:

real and inverted

Explanation:

when we use the mirror formula, we get -20, the minus depicts that the image lies in the opposite direction which is real and inverted

Hope it helps!☺️

Answer 2

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Given:}}}$

• Mirror given is a concave mirror
• Object Distance = 20cm
• Focal length = 10 cm

$\large\underline{\sf{\blue{To \: Find:}}}$

• We have to find the nature of image

$\large\underline{\sf{\blue{Concept \: Used:}}}$

Mirror Formula:

This is an equation relating the object distance and image distance with focal length is known as mirror equation

$\large\boxed{\sf{\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}}}$

$\sf{}$

$\large\underline{\sf{\blue{Solution:}}}$

Given that , an object is placed at a distance of 20cm from a concave mirror of focal length 10cm

Using sign convention

• Object Distance = -20 cm
• Focal Length = -10 cm

$\sf{}$

$\large\underline{\mathfrak{\red{Using \: Mirror \: Formula:}}}$

We have to put the given values in Mirror Formula with proper sign convention

$\implies \sf{\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}}$

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

$\implies \sf{\dfrac{1}{v} = \dfrac{1}{-10} - \dfrac{1}{-20}}$

$\implies \sf{\dfrac{1}{v} = -\dfrac{1}{10} + \dfrac{1}{20}}$

Taking LCM on Right hand of Equation

$\implies \sf{\dfrac{1}{v} = \dfrac{1 - 2}{20}}$

$\implies \sf{\dfrac{1}{v} = - \dfrac{1}{20}}$

Reciprocaling both sides of Equation

$\implies \boxed{\sf{v = - 20 \: cm}}$

Image is formed at a distance of 20 cm in front of mirror

$\sf{}$

$\large\underline{\mathfrak{\red{Magnification:}}}$

$\hookrightarrow \sf{m = - \dfrac{v}{u}}$

$\hookrightarrow \sf{m = - \left ( \dfrac{-20}{-20} \right ) }$

$\hookrightarrow \boxed{\sf{m = - 1 }}$

$\sf{}$

Nature of Image Formed:

• Real and Inverted
• Identical in size
• At a distance of 20 cm in front of mirror

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