Question 29 of 29beginner🔧 ApplyNumerical2 marks

A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?

Correct Answer

Given: Power of lens, P = +1.5 D

To find: Focal length of the lens and its nature.

Formula: P = 1/f

Calculation: f = 1/P = 1/(+1.5) = +0.67 m (or +66.7 cm)

Nature of lens: The power of the prescribed lens is positive (+1.5 D). According to the text, the power of a convex lens is positive and that of a concave lens is negative. A convex lens converges light rays. Therefore, the prescribed lens is converging.

Exercise: EXERCISES | Q: 17 | (Page Page 27)
For More Understanding

Explanation

This is a straightforward application of the power-focal length relationship. The formula P = 1/f is given in the textbook context. Since power is positive, the focal length must also be positive, indicating a convex lens. The context explicitly states that 'the power of a convex lens is positive' and convex lenses are converging lenses that focus light rays closer to the optical centre.

Solution Steps

  1. Step 1: Write the given value: Power P = +1.5 D

  2. Step 2: Apply the formula P = 1/f, rearranged as f = 1/P

  3. Step 3: Calculate: f = 1/(+1.5) = +0.67 m

  4. Step 4: Identify lens type: Since power is positive, it is a convex lens

  5. Step 5: Conclude: Convex lens is a converging lens

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