An object is placed 24\text{ cm} in front of a concave mirror with a focal length of 8\tex… — JAMB UTME

An object is placed $24\text{ cm}$ in front of a concave mirror with a focal length of $8\text{ cm}$ . What is the distance of the image from the mirror in $\text{cm}$ ?

Answer: 12 cm

Answer

The distance of the image from the mirror is

12\text{ cm}

Applying the spherical mirror formula

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

with focal length

f = 8\text{ cm}

and object distance

u = 24\text{ cm}

yields

\frac{1}{v} = \frac{1}{8} - \frac{1}{24} = \frac{1}{12}

, giving an image distance of

12\text{ cm}

Step-by-Step Solution

Identify the given parameters and select the appropriate relation.

Focal length

f = 8\text{ cm}

, object distance

u = 24\text{ cm}

, using the mirror equation

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

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

Substitute the given values into the formula and solve for

\frac{1}{v}

\frac{1}{8} = \frac{1}{24} + \frac{1}{v} \implies \frac{1}{v} = \frac{1}{8} - \frac{1}{24} = \frac{3-1}{24} = \frac{2}{24} = \frac{1}{12}

Subtracting

\frac{1}{24}

from

\frac{1}{8}

isolates the reciprocal of the image distance.

Invert the result to determine the image distance

v

v = 12\text{ cm}

Taking the reciprocal of

\frac{1}{12}

gives the image distance in centimeters.

Key Concept

Mirror Formula for Concave Mirrors

Estimated Time:45s

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