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An object is \(6.0 \mathrm{~cm}\) from a thin lens along the axis of the lens. If the lens has a focal length of \(9.0 \mathrm{~cm},\) determine the image distance.

Short Answer

Expert verified
Answer: The image distance is -18 cm, and it is a virtual image located on the same side as the object.

Step by step solution

01

Write down the thin lens formula

\(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\)
02

Plug in the values of f and d_o

\(\frac{1}{9.0} = \frac{1}{6.0} + \frac{1}{d_i}\)
03

Solve for d_i

First, subtract \(\frac{1}{6.0}\) from both sides of the equation: \(\frac{1}{9.0} - \frac{1}{6.0} = \frac{1}{d_i}\) Now, find the common denominator (which is 18) and simplify: \(\frac{2-3}{18} = \frac{1}{d_i}\) So, we have: \(\frac{-1}{18} = \frac{1}{d_i}\) Finally, reciprocate both sides of the equation to find the image distance: \(d_i = -18 \mathrm{~cm}\)
04

Interpret the result

The image distance is \(-18\) cm. The negative sign indicates that the image is on the same side as the object, in other words, it's a virtual image.

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