An object is placed at a distance of 15\text{ cm} in front of a concave mirror with a foca… — JAMB UTME

An object is placed at a distance of $15\text{ cm}$ in front of a concave mirror with a focal length of $10\text{ cm}$ . What is the distance of the image formed from the mirror?

$30\text{ cm}$ Answer
B
$6\text{ cm}$
C
$25\text{ cm}$
D
$-30\text{ cm}$

Answer

The distance of the image formed from the mirror is

30\text{ cm}

Applying the mirror formula

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

with

f = 10\text{ cm}

and

u = 15\text{ cm}

gives

\frac{1}{v} = \frac{1}{10} - \frac{1}{15} = \frac{1}{30}

, yielding an image distance of

30\text{ cm}

Step-by-Step Solution

Identify given quantities and signs

Focal length

f = 10\text{ cm}

and object distance

u = 15\text{ cm}

For a concave mirror, the real focus and real object distances are both positive.

Set up the mirror formula

\frac{1}{f} = \frac{1}{u} + \frac{1}{v} \implies \frac{1}{10} = \frac{1}{15} + \frac{1}{v}

The mirror formula relates object distance, image distance, and focal length.

Solve for the image distance

v

\frac{1}{v} = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30} \implies v = 30\text{ cm}

Subtracting the reciprocals and taking the inverse gives the image position.

Key Concept

Concave Mirror Formula

Question

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Step-by-Step Solution

Key Concept

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