MP Board · Class 10 · Science · The Human Eye and Colourful WorldCalculate the power of a concave lens whose focal length is $-50\text{ cm}$. State the formula used and explain what the negative sign indicates.

Given:

• Focal length of the concave lens ($f$) = $-50\text{ cm}$ \nFirst, convert the focal length into meters: $$f = \frac{-50}{100}\text{ m} = -0.5\text{ m}$| \nFormula for the power of a lens ($P$): $$P = \frac{1}{f\text{ (in meters)}}$| \nSubstitute the value of $f$ into the formula: $$P = \frac{1}{-0.5\text{ m}} = -2.0\text{ D}$| \nExplanation of the Negative Sign:
• The negative sign associated with the power indicates that the given lens is a concave lens (diverging lens).
• A concave lens always has a virtual focus located in front of the lens, resulting in a negative focal length and consequently a negative optical power value.