Question

when an object is placed at a distance of 50cmfrom a concave mirror uts image is formed at 10cm in front of the mirror Calculate the focal length of the mirror
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Answer 1

Given :

▪ Distance of object = -50cm

▪ Distance of image = -10cm

▪ Type of mirror : concave

To Find :

▪ Focal length of the mirror

Formula :

✴ Mirror formula :

$\bigstar\:\underline{\boxed{\bf{\purple{\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}}}}}$

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

Calculation :

$:\implies\sf\:\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\\ \\ :\implies\sf\:\dfrac{1}{(-10)}+\dfrac{1}{(-50)}=\dfrac{1}{f}\\ \\ :\implies\sf\:\dfrac{1}{f}=\dfrac{-5-1}{50}\\ \\ :\implies\sf\:f=-\dfrac{50}{6}\\ \\ :\implies\underline{\boxed{\bf{\green{f=-8.33cm}}}}\:\orange{\bigstar}$

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▶ Extra Dose :

• X-coordinate of centre of curvature and focus of Concave mirror are negative and those for Convex mirror are positive.
• In case of mirrors since light rays reflects back in X-direction, therefore -ve sign of v indicates real image and +ve sign of v indicates virtual image.

Answer 2

Aɴꜱᴡᴇʀ

☞ F = (-8.33 cm)

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Gɪᴠᴇɴ

➢ Distance between the object and mirror (u) = -50 cm

➢ Distance of image (v) = -10 cm

➢ Mirror used = Concave mirror

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Tᴏ ꜰɪɴᴅ

◕ Focal Length of the mirror?

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Sᴛᴇᴘꜱ

❍ Your answer can be found with the help of Mirror Formula, that is,

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

Substituting the given values,

$\dashrightarrow\sf\dfrac{1}{v}+\dfrac{1}{u} = \frac{1}{f}\\ \\ \dashrightarrow\sf\dfrac{1}{(-10)}+\dfrac{1}{(-50)}= \dfrac{1}{f}\\ \\ \dashrightarrow\sf\frac{1}{f} =\dfrac{-5-1}{50}\\ \\ \dashrightarrow\sf f =- \frac{50}{6}\\ \\ \pink{\dashrightarrow{\sf{f=-8.33cm}}}$

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Additional Information:-

➤ More about mirrors

✭ There are 3 kinds of mirrors

↣ Convex

↣ Concave

↣ Plane

✭ In concave mirrors the reflected rays meet at a point that is called the focus

✭ In car headlights concave mirrors are used (they are not exactly concave but parabolic shape)

➤ More about light

☆ Light always travels in a straight line

➳ This can be proved using the Fermat's Principle of least time

✪ Between two points light always takes the shortest path.

☆ Bending of light is called "Refraction"

☆ Bouncing back of light is called "Reflection"

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