Solutions to Homework Problem set #6.

Chapter 4, pages 142-143: P6, P7, PM1, PM2, PM3

P6. (a) The amount of light that strikes the film is proportional to the reciprocal of the square of the f/number and is linearly proportional to the exposure time. Therefore, increasing the f/number by a factor of 2 (from f/5.6 to f/11) decreases the amount of light striking the film by 4. This decrease can be compensated by increasing the exposure time by the same factor of 4 from 1/100 s to 1/25 s.

(b) Other valid combinations could be gotten using other factors of 2 either up or down from f/5.6 at 1/100. For example, f/2.8 at 1/400 or f/1.4 at 1/1600, etc. You could also change the f/number by the square root of 2 and change the exposure by 2. For example f/8 at 1/50.

P7. All of the combinations are related to each other by changes in the f/number of the square root of 2 and changes in the exposure 2 by a factor of 2. Therefore they are all equivalent.

(a) When the object is in motion, you would choose the combination with the fastest shutter speed to minimize the blurring of the image. This would be f/2 at 1/200 s.

(b) The goal would be to maximize the depth of field so that all of the flowers would be in focus at the same time. You would choose the combination with the smallest lens opening (largest f/number) in this case. This would be f/5.6 at 1/25 s.

(c) The goal would be to minimize the depth of field so that you could bring the animal into sharp focus and have the bars out of focus. You would choose the combination with the largest lens opening (smallest f/number) in this case. This would be f/2 at 1/200 s.

PM1. The f/number is defined as the focal length divided by the diameter. If the diameter is d, then 56/d= 5.6. Then d= 56/5.6= 10 mm.

PM2. As in previous problem, f/number is focal length divided by the diameter. If focal length is f, then f/28= 1.8, so that f=28*1.8= 50.4 mm.

(b) If you double the focal length, you must double the diameter to keep the ratio the same. Thus the new diameter would be double 28 mm or 56 mm.

PM3. (a) f/number is ratio of focal length to diameter. Thus f/number= 120/7.5= f/16.

(b) f/number= 120/15= f/8.

(c) If the diameter of the largest opening is d, then 120/d= 4. Thus d=120/4= 30 mm.