Final answer:
To correct nearsightedness for Mr. Barnabas whose far point is 85 cm away, we calculate the focal length required for eyeglasses, which should have a power of -1.20 diopters.
Step-by-step explanation:
Mr. Barnabas is nearsighted with a far point located at 85 cm from his eye. To correct his vision so that he can see distant objects, we need to calculate the focal length of the eyeglasses that he needs to wear. These glasses are held 2 cm in front of his eyes.
For a nearsighted person, the glasses need to have a diverging lens which will create an image of the distant objects at his far point. Since the far point of Mr. Barnabas is at 85 cm, the glasses should form the image at this distance when viewing distant objects (which are essentially at infinity).
The lens formula is given by 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. For distant objects, u approaches negative infinity, and we can consider the term 1/u as 0. Thus, the formula simplifies to f = v. However, the effective image distance for glasses is the far point distance (85 cm) minus the distance the glasses are in front of the eyes (2 cm), which equals 83 cm.
The correct focal length for Mr. Barnabas's glasses would then be -83 cm (negative because it is a diverging lens). To find the power of the spectacle lens (P), we use the formula P = 1/f (with f in meters). So, P = -1/0.83, giving us approximately -1.20 diopters (D), which means the spectacle lenses should have a power of -1.20 D.