The author has an inexpensive digital camera that has the following specifications: “5X optical zoom, 7X digital zoom.” 

(a) The “lens” is actually a combination of several lenses, and the value of the optical zoom is adjusted by changing the focal length f of the lens system. If the magnification is changed by a factor of five (the maximum optical zoom), by what factor does f change? 

(b) The digital zoom is adjusted by using the image from only a portion of the CCD detector. When the digital zoom is “off,” all the CCD’s pixels are used. What fraction of the pixels is used when the digital zoom is set for its maximum value (7X)?