Question

If a convex lens of focal length 80 cm and a concave lens of focal length 50 cm are combined together, what will be their resulting power?

• A. #ERROR!
• B. -0.75 D
• C. #ERROR!
• D. -6 .5 D.

Answer 1

The Correct Option is B

To find the resulting power of a combination of a convex lens and a concave lens, we use the formula for the power of lenses in combination:

P_{\text{total}} = P_1 + P_2

Where:

• P_1 is the power of the convex lens.
• P_2 is the power of the concave lens.

The power P of a lens is given by the formula:

P = \frac{1}{f}

where f is the focal length in meters. Thus, we first need to convert the focal lengths from cm to meters:

• Focal length of convex lens, f_1 = 80\, \text{cm} = 0.80\, \text{m}
• Focal length of concave lens, f_2 = -50\, \text{cm} = -0.50\, \text{m} (Negative sign because the lens is concave.)

Calculating the power of each lens separately:

• Power of the convex lens: P_1 = \frac{1}{0.80} = 1.25\, \text{D}
• Power of the concave lens: P_2 = \frac{1}{-0.50} = -2.0\, \text{D}

Now, calculate the total power:

P_{\text{total}} = P_1 + P_2 = 1.25 + (-2.0) = -0.75\, \text{D}

Therefore, the resulting power of the combined lenses is -0.75\, \text{D}.

This confirms that the correct answer is -0.75 D.