Question

A concave lens of focal length $15cm$ forms an image $10cm$ from the lens. How far is the object placed from the lens? Draw the ray diagram.

Answer 1

Step 1:Given data-

Focal length, $f=-15cm$

Focal length of concave lens is always negative.

Image distance, $v=-10cm$

Image distance of a concave lens is also negative.

Step 2:Formula applied

Applying lens formula

$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{-15}=\frac{1}{-10}-\frac{1}{u} \\ \frac{1}{u}=\frac{-1}{10}+\frac{1}{15} \\ \frac{1}{u}=\frac{-15+10}{150} \\ \frac{1}{u}=\frac{-5}{150} \\ \frac{1}{u}=\frac{-1}{30} \\ u=-30cm \end{gathered}$$

Negative sign is because the object is on the left side of the lens (sign convention)

Ray diagram

The diagram shows that the image is formed on the same side as the object and we should have taken the image distance as negative.

Image is formed between focus and pole and is shorter than the object's height

Therefore, image distance from the lens is $30cm$on the left side of the lens.