Lenses 2: Thin Lens Equation Lesson 10 November 24th, 2010

Thin Lens Equation The distance of the object from the lens, do, the distance of the image from the lens, di, and the focal length of a lens, f , can all be related using the thin lens equation. Given any two of these quantities, you can use the thin lens equation to solve for the third: 1 = 1 + 1 ƒ do di

Thin Lens Equation Keep in mind the following points when working with the thin lens equation A concave lens has a negative focal length and a negative distance to the image. A convex lens has a positive focal length and either a positive or negative distance to the image, depending where the object is placed. The image distance di is positive if the image is real and negative if the image is virtual.

Example Problem 1 Focal length of the lens, f =? A convex lens of a magnifying glass is held 2.00 cm above a page to magnify the print. If the image produced by the lens is 3.60 cm away and virtual, what is the focal length of the magnifying glass? G Distance of the object from the lens, do = 2.00 cm Distance of the virtual image from the lens, di = -3.60 cm S Take the reciprocal of both sides f =4.50 cm R Focal length of the lens, f =? P Therefore, The focal length is about 4.50 cm. A 1 = 1 + 1 ƒ do di

Example Problem 2 Focal length of the convex lens, f = 60 cm A convex lens has a focal length of 60.0 cm. A candle is placed 50 cm from the lens. What type of image is formed, and how far is the image from the lens? G Focal length of the convex lens, f = 60 cm Distance of the object from the lens, do = 50 cm S Take the reciprocal from each side di = -300 cm R Distance of the image from the lens, di = ? P Therefore, since di is negative, the image is virtual and is located 300 cm from the lens. A 1 = 1 + 1 ƒ do di

Example Problem 3 Focal length of lens, f = 200 mm A camera with a 200-mm lens makes a real image of a bird on film. The film is located 201 mm behind the lens. Determine the distance from the lens to the bird. G Focal length of lens, f = 200 mm Image distance, di = 201mm S Take the reciprocal of each side = do = 4.02 x104 mm R Object distance of the bird from the lens, do = ? P Therefore, the bird is about 40.2 m away from the camera lens A 1 = 1 + 1 ƒ do di

Focal Length: Lab Purpose To find a good approximation of the focal length of any convex lens and see the relationship between the curvature of the lens and the focal length