=388. The Lens Equation.=--The location of either the object or of the image upon the principal axis of the lens may be calculated if the position of one of these and the focal length are known. This is accomplished by the use of a formula 1/_F_ = 1/_D_{0}_ + 1/_D_{1}_ in which _F_ represents the focal length and _D_{0}_ and _D_{1}_ the distance from the lens of the object and the image respectively. Thus if an object is placed 30 cm. from a lens of 10 cm. focal length, where will the image be formed? Thus: 1/10 = 1/30 + 1/_D_ and 3_D_{1}_ = _D_{1}_ + 30, or 2_D_{1}_ = 30 _D_{1}_ = 15. This result indicates that a real image will be 15 cm. from the lens. A minus value would indicate a virtual image. Important Topics (A) Lenses: convex, concave, six forms, center and radius of curvature. (B) Principal focus, focal length, virtual focus, conjugate foci. (C) Principal axis, images formed when object is in various locations. (D) Computation of location of images. Exercises 1. Why is an image of a candle formed by an aperture, not sharply defined? 2. When a photographer takes your picture and moves the camera nearer you, must he move the ground glass screen toward the lens or away from it? Explain. 3. How can you find the principal focal length of a lens. 4. How can you test a spectacle lens to see whether it is convex concave? 5. When will a convex lens produce a virtual image? Have you ever seen one? Where? 6. When a photographer wishes to obtain a full length view of a person, where does he place the camera? 7. The focal length of the lens is 24 cm. How far from the lens must an object be placed in order that a real image may be three times as long as the object? 8. There is a perfect image of an object on the ground glass of a camera. The center of the lens is 20 cm. in front of the image and the object 75 cm. from the lens. What is the focal length of the lens? 9. An object is 60 cm. from the lens, the image 120 cm. from it. Find the focal length. 10. How can you find experimentally the principal focal length of a lens? 11. A lens is used to project an enlarged image of a candle upon a screen. Which is farther from the lens, the candle or the image? Explain. (6) OPTICAL INSTRUMENTS =389. The Eye.=--The most common optical instrument is the _eye_. While the structure of the eye is complicated, the principle of it is simple, involving the formation of an image by a double convex lens. (See Fig. 386, in which is shown a front to back, vertical cross-section of the eye.) The eye appears to be made of portions of two spheres, one of which, smaller than the other, is placed in front. This projecting part is transparent, but refracts the light which strikes it obliquely, so as to turn it into the eye. This enables us to see objects at the side when looking straight ahead. Test this by looking directly in front of you and see how far back on each side of the head you can notice a movement of the forefinger of each hand.