A diverging lens of focal length 30cm produces an image 20cm from the lens. Determine the object distance
- 10cm
-
12cm
- 50cm
- 60cm
The correct answer is: B
Explanation
Lens formula:
\(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\)
where f, d\(_o\) and d\(_i\) are the focal length, object distance and image distance respectively.
The distance from the lens to the focal point is called the focal length. For converging lenses, the focal length is always positive, while diverging lenses always have negative focal lengths.
⇒ \(\frac{-1}{30} = \frac{1}{d_o} + \frac{1}{20}\)
\(\frac{1}{d_o} = \frac{-1}{30} - \frac{1}{20}\)
\(\frac{1}{d_o} = \frac{-2 + -3}{60}\)
→ \frac{-5}{60}\) = \frac{-1}{12}\)
\(d_o = - 12 cm\)
The object distance -12cm = 12cm on the other side of the lens.