Far vision Near vision Figure P25.18

Problem 6:  Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as visible light.  Find the magnification of the heater element, given that the mirror has a radius of curvature of 49 cm and produces an image of the coils 3.2 m away from the mirror.

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A patient with a refractive myopia cannot see objects clearly if they are further away than 10 m. To be able to drive safely and obtain his driving license, he needs to be able to clearly see objects up to 100 m away. In this problem, Pmin eye = minimum optical power of the patient’s natural eyes, Pmin combo = minimum optical power of the patient’s natural eyes + corrective glasses, and Pmin glasses =  minimum optical power of the corrective glasses. Calculate the focal length.

A patient with a refractive myopia cannot see objects clearly if they are further away than 10 m. To be able to drive safely and obtain his driving license, he needs to be able to clearly see objects up to 100 m away. In this problem, Pmin eye = minimum optical power of the patient’s natural eyes, Pmin combo = minimum optical power of the patient’s natural eyes + corrective glasses, and Pmin glasses =  minimum optical power of the corrective glasses Calculate the minimum combined optical power for the patient’s eyes plus their corrective glasses (Pmin combo) that is required for the patient to see an object at 100 m.

An office administrator realizes that she is having trouble doing her work due to eyesight problems. Her optometrist determines that without glasses she can focus clearly only on objects that lie at distances between 0.450 m and 4.00 m. The optometrist decides that the best way to handle her eyesight problems is to prescribe bifocals that will give her normal visual acuity from 25.0 cm out to infinity. After trying on several pairs of glasses frames, they agree that the glasses will be a distance of 2.20 cm from her eyes. (a) Determine the refractive power needed for the bifocal part that will correct for her nearsightedness (include the sign). D What type of lens is needed? O converging O diverging (b) Determine the refractive power needed for the bifocal part that will correct for her farsightedness (include the sign). D What type of lens is needed? O converging diverging

A small telescope has a concave mirror with a 2.6 m radius of curvature for its objective. Its eyepiece is a 3.4 cm focal length lens.  Part (b)  What angle (in degrees) is subtended by a 25,000 km diameter sunspot? Assume the sun is 1.50 × 108 km away.   Part (c)  What is the image angular size (in degrees) in this telescope?

A laser beam of diameter d₁-1.1 mm is directed along the optical axis of a thin lens of focal length +4.7 cm (see figure below). (a) How far from the lens will the beam be focused? (b) A second positive lens is placed to the right of the first. Light emerges from the second lens in a parallel beam of diameter dy 3.6 mm. Thus the combination of lenses acts as a beam expander. Find the focal length of the second lens. Find the distance between the lenses.