Question

What is the focal length f of this lens in air (index of refraction for air is nair=1)? express your answer in centimeters to two significant figures or as a fraction?

Answer 1

The complete question is:
"A convex-convex lens has radii of curvature with magnitudes of |R₁| = 10 cm and |R₂| = 15 cm. The lens is made of glass with an index of refraction n_glass = 1.5. We will employ the convention that R₁ refers to the radius of curvature of the surface through which light will enter the lens, and R₂ refers to the radius of curvature of the surface from which light will exit the lens."

The focal length can be calculated by the formula:
$\frac{1}{f} = ( \frac{n_{glass} }{ n_{air} } - 1)( \frac{1}{ R_{1} } + \frac{1}{ R_{2} } )$
= (1.5 - 1)(1/10 + 1/15)
= 1/12

Therefore, the focal length of the lens is f = 12 cm.