An object is placed 12\text{ cm} in front of a concave mirror having a focal length of 20\… — JAMB UTME

An object is placed $12\text{ cm}$ in front of a concave mirror having a focal length of $20\text{ cm}$ . What is the distance of the image from the mirror and its nature?

$30\text{ cm}$ behind the mirror, virtualCevap
B
$30\text{ cm}$ in front of the mirror, real
C
$7.5\text{ cm}$ in front of the mirror, real
D
$7.5\text{ cm}$ behind the mirror, virtual

Cevap

The image is formed

30\text{ cm}

behind the mirror and is virtual.

Applying the mirror formula

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

with

f = 20\text{ cm}

and

u = 12\text{ cm}

yields

\frac{1}{v} = \frac{1}{20} - \frac{1}{12} = -\frac{1}{30}\text{ cm}^{-1}

, resulting in

v = -30\text{ cm}

. The negative sign confirms that the image is virtual and located

30\text{ cm}

behind the mirror.

Adım Adım Çözüm

Identify given quantities and apply standard mirror sign conventions.

Object distance

u = +12\text{ cm}

, focal length

f = +20\text{ cm}

For a concave mirror, real objects and real focal points carry positive values.

Set up the mirror equation

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

\frac{1}{20} = \frac{1}{12} + \frac{1}{v}

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

Rearrange the equation to isolate

\frac{1}{v}

and solve.

\frac{1}{v} = \frac{1}{20} - \frac{1}{12} = \frac{3 - 5}{60} = -\frac{2}{60} = -\frac{1}{30}\text{ cm}^{-1} \implies v = -30\text{ cm}.

Finding a common denominator of 60 allows exact calculation of the negative reciprocal.

Determine image characteristics based on the sign of

v

The image distance magnitude is

30\text{ cm}

behind the mirror, and the image is virtual.

A negative value for image distance

v

signifies a virtual image located behind the mirror surface.

Anahtar Kavram

Concave Mirror Formula and Virtual Image Formation

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru