A lens system in air has a +4.00 diopter and a +6.00 diopter lens separated by 10cm. What is the equivalent power of this optical system?

To find the equivalent power of a lens system in air, we can utilize the formula for the combined power of two thin lenses separated by a distance:

1. First, convert the powers of the lenses from diopters to their respective focal lengths in meters:

• The focal length (f) of the +4.00 diopter lens is given by f = 1/P = 1/4.00 m = 0.25 m.

• The focal length (f) of the +6.00 diopter lens is given by f = 1/P = 1/6.00 m ≈ 0.1667 m.

2. Next, since the lenses are separated by a distance (d) of 10 cm (or 0.1 m), the effective focal length of the optical system can be calculated using the formula for two lenses in combination:

[ P_{\text{total}} = P_1 + P_2 - \frac{d}{f_1 f_2} ]

where ( P_1 ) and ( P_2 ) are the powers of the individual lenses, and ( d ) is the separation distance.

3. Plugging in