Answer:
0.05 dioptre
Explanation:
To find the power of the convex lens, we can use the lens formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Where:
- \( f \) is the focal length of the lens,
- \( v \) is the image distance (positive if the image is formed on the opposite side of the object),
- \( u \) is the object distance (positive if the object is on the same side as the incoming light).
Given:
\( u = -60 \) cm (since the object is placed in front of the lens),
\( v = 30 \) cm (since the image is formed behind the lens).
Now, plug the values into the lens formula:
\[ \frac{1}{f} = \frac{1}{30} - \frac{1}{-60} \]
\[ \frac{1}{f} = \frac{1}{30} + \frac{1}{60} \]
\[ \frac{1}{f} = \frac{2}{60} + \frac{1}{60} \]
\[ \frac{1}{f} = \frac{3}{60} \]
\[ \frac{1}{f} = \frac{1}{20} \]
\[ f = 20 \text{ cm} \]
Now, the power of the lens (in dioptres) is given by:
\[ P = \frac{1}{f} \]
\[ P = \frac{1}{20} \]
\[ P = 0.05 \text{ dioptre} \]
So, the correct answer is ii) 0.05 dioptre.
