A convex lens of power 3 D is held in contact with a concave lens of power -1D.A parallel beam of light is made to fall on the combination. At what distance from the combination will the beam get focussed?

Options

A. `20cm`
B. `60cm`
C. `50cm`
D. `90cm`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the Lens Powers
We have a convex lens with a power of +3 D and a concave lens with a power of -1 D.

### Step 2: Calculate the Total Power of the Combination
The total power \( P_{total} \) of the lens combination can be calculated by adding the individual powers of the lenses:
\[ P_{total} = P_{convex} + P_{concave} = +3 D + (-1 D) = +2 D \]

### Step 3: Determine the Focal Length of the Combination
The focal length \( f \) of a lens is related to its power \( P \) by the formula:
\[ P = \frac{1}{f} \]
Rearranging this gives us:
\[ f = \frac{1}{P} \]
Since we need the focal length in meters, we first convert the power from diopters to focal length:
\[ f = \frac{1}{2} \text{ meters} = 0.5 \text{ meters} = 50 \text{ centimeters} \]

### Step 4: Conclusion
The parallel beam of light will focus at a distance of 50 centimeters from the lens combination.

### Final Answer
The beam will get focused at a distance of 50 cm from the combination.

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