a convex lens of power `+6` dioptre is placed in contact with a concave lens of power`-4` dioptre. What will be the nature and focal length of this combination?

Options

A. Concave, 25cm
B. Convex, 50cm
C. Concave, 20cm
D. Convex, 100cm

Explanation

To solve the problem of finding the nature and focal length of a combination of a convex lens and a concave lens, we can follow these steps:

### Step 1: Identify the powers of the lenses
- The power of the convex lens (P1) is +6 diopters.
- The power of the concave lens (P2) is -4 diopters.

### Step 2: Calculate the total power of the combination
The total power (P) of the combination of lenses in contact is given by the sum of their individual powers:
\[ P = P_1 + P_2 \]
Substituting the values:
\[ P = +6 \, \text{D} + (-4 \, \text{D}) \]
\[ P = 6 - 4 = 2 \, \text{D} \]

### Step 3: Calculate 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:
\[ f = \frac{1}{P} \]
Substituting the total power we found:
\[ f = \frac{1}{2 \, \text{D}} \]
\[ f = 0.5 \, \text{m} \text{ or } 50 \, \text{cm} \]

### Step 4: Determine the nature of the combination
Since the total power of the combination is positive (+2 D), the focal length is also positive (50 cm). This indicates that the combination behaves like a convex lens.

### Final Answer
The nature of the combination is a convex lens, and the focal length is 50 cm.

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