Shashank went to the optician to get his eyes checked. He observed that the doctor combined two lenses and put these in front of his eyes so that he could see clearly. The powers of the two lenses used in the combination were -3 D and 4 D.
Which of these will be the focal length of the combination of lenses Shashank has to wear?

Options

A. `-14 cm`
B. `+25 cm`
C. `-33 cm`
D. `+100 cm`

Answer

To find the focal length of the combination of lenses that Shashank has to wear, we will follow these steps:

### Step 1: Understand the given data
We have two lenses with the following powers:
- Power of lens 1 (P1) = -3 D (diopters)
- Power of lens 2 (P2) = +4 D (diopters)

### Step 2: Use the formula for the power of a lens
The power (P) of a lens is related to its focal length (F) by the formula:
\[ P = \frac{1}{F} \]
where F is in meters.

### Step 3: Calculate the focal lengths of the individual lenses
Using the formula, we can find the focal lengths of the individual lenses:
- For lens 1:
\[ P1 = \frac{1}{F1} \Rightarrow F1 = \frac{1}{P1} = \frac{1}{-3} = -\frac{1}{3} \text{ m} \]
- For lens 2:
\[ P2 = \frac{1}{F2} \Rightarrow F2 = \frac{1}{P2} = \frac{1}{4} = \frac{1}{4} \text{ m} \]

### Step 4: Use the formula for the power of the combination of lenses
The total power (P_total) of the combination of lenses is given by:
\[ P_{total} = P1 + P2 \]

### Step 5: Calculate the total power
Now we can calculate the total power:
\[ P_{total} = -3 + 4 = 1 \text{ D} \]

### Step 6: Find the focal length of the combination
Using the power of the combination, we can find the focal length of the combination:
\[ P_{total} = \frac{1}{F_{total}} \Rightarrow F_{total} = \frac{1}{P_{total}} = \frac{1}{1} = 1 \text{ m} \]

### Step 7: Convert the focal length to centimeters
Since 1 meter is equal to 100 centimeters:
\[ F_{total} = 100 \text{ cm} \]

### Conclusion
The focal length of the combination of lenses that Shashank has to wear is **100 cm**.

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