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 find the nature and focal length of the 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, and 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 formula:
\[ P = P_1 + P_2 \]

Substituting the values:
\[ P = 6 \, \text{D} + (-4 \, \text{D}) \]
\[ P = 6 - 4 = 2 \, \text{D} \]

### Step 3: Determine the nature of the combination
Since the total power is positive (+2 D), the combination behaves like a convex lens.

### Step 4: Calculate the focal length of the combination
The relationship between power (P) and focal length (f) is given by:
\[ P = \frac{1}{f} \]
Where \( f \) is in meters. To find \( f \) in centimeters, we can use:
\[ P = \frac{100}{f} \]

Rearranging the formula to find \( f \):
\[ f = \frac{100}{P} \]

Substituting the value of power:
\[ f = \frac{100}{2} = 50 \, \text{cm} \]

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

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