An object is placed 15.0\text{ cm} in front of a thin diverging lens with a focal length o… — JAMB UTME

An object is placed $15.0\text{ cm}$ in front of a thin diverging lens with a focal length of $10.0\text{ cm}$ . What is the image distance formed by the lens?

$-6.0\text{ cm}$ ( $6.0\text{ cm}$ on the same side as the object)Answer
B
$+30.0\text{ cm}$ ( $30.0\text{ cm}$ on the opposite side of the object)
C
$+6.0\text{ cm}$ ( $6.0\text{ cm}$ on the opposite side of the object)
D
$-30.0\text{ cm}$ ( $30.0\text{ cm}$ on the same side as the object)

Answer

The image distance is

-6.0\text{ cm}

, indicating a virtual image located

6.0\text{ cm}

in front of the lens on the same side as the object.

Using the thin lens equation

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

with

u = +15.0\text{ cm}

and

f = -10.0\text{ cm}

for the diverging lens gives

\frac{1}{v} = -\frac{1}{10} - \frac{1}{15} = -\frac{1}{6}

, resulting in

v = -6.0\text{ cm}

. The negative sign confirms the image is virtual and formed on the same side as the object.

Step-by-Step Solution

Identify the given optical parameters and apply the proper sign convention.

Object distance

u = +15.0\text{ cm}

; Focal length for a diverging lens

f = -10.0\text{ cm}

By the real-is-positive sign convention, real object distance

u

is positive, while the focal length

f

of a concave/diverging lens is strictly negative.

Set up the thin lens formula

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

and solve for

\frac{1}{v}

\frac{1}{-10.0} = \frac{1}{15.0} + \frac{1}{v} \implies \frac{1}{v} = -\frac{1}{10.0} - \frac{1}{15.0}

Isolating the reciprocal image distance term requires subtracting

\frac{1}{u}

from both sides.

Calculate the common denominator and evaluate

v

\frac{1}{v} = \frac{-3 - 2}{30.0} = -\frac{5.0}{30.0} = -\frac{1}{6.0} \implies v = -6.0\text{ cm}

Inverting the reciprocal yields the final signed image distance.

Key Concept

Thin Lens Formula and Sign Conventions for Diverging Lenses

Estimated Time:1m 15s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic