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    Refraction, Lenses and Eysight

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    3. Your significant other (SO) meets you sporting a new set of glasses. YOu never realized that she/he needed glasses at all, but the person sought the advice of a physician because he/she had headaches at the end of the day. Referral to an optometrist resulted in glasses. You pick up the prescription from his/her desk and examine it closely. You find the glasses increase the size of the objects as you look through the lenses held at reading distance away, and that the object seen through the lenses distorts as you rotate the glasses int he plane of the surface of the lenses. The prescription reads:
    OD + 2.0 -0.5 x 98 degrees
    OS + 2.75 - 1.25 x 160 degrees.

    Diagnose your SO's refractive errors in technically correct language, and tell why these glasses may alleviate his/her evening headaches.

    6. You are on the City Council, and are known to be an engineer. Your advice is sought as to the design of street marker signs in your city. The night-time street illumination is very subdued, so consideration is given to using high efficiency reflecting material either for the backgrounds or for the letters of these signs, so drivers can read the signs in the peripheral illumination provided from headlamps. Assuming adequate contrast, how tall should these letters be to legible from 100 ft away by drivers who have unrestricted drive licenses in Texas, and thus test at least 20/50?

    8. In question 6 above, suppose that street sign is located 100 ft (horizontal distance, not line-of-sight) from a street luminaire. The luminaire is mounted on a power pole 20 ft above the street. To put at least 0.5 ft candle illuminance on the sign (which is mounted on a post 10ft high) what is the intensity of the luminaire?

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    Solution Preview

    You should likely have all the necessary definitions and formulae in your book(s) and lecture notes. However, just in case, here are web pages where the necessary definitions and formulae can also be found:

    for question 3:

    for question 6:

    for question 8:

    Here are the explanations:

    Question 3:
    The prescription reads:

    Right eye:
    Spherical correction +2.0 diopters
    Cylindrical correction -0.5 diopters with cylinder axis at 98 degrees

    Left eye:
    Spherical correction +2.75 diopters
    Cylindrical correction -1.25 diopters with ...

    Solution Summary

    This solution interprets the prescription and explains the refractive errors in technically correct language and how the glasses alleviate headaches. It also calculates how tall the letters need to be so drivers can read them from 100 ft away and what the intensity of the luminaire is. All steps and workings are shown with brief explanations.