Lens Maker’s formula 1/f=(μ – 1) (1/R 1 – 1/R 2) where, μ = refractive index of the material of the lens and R 1 and R 2 are radii of curvature of the lens. The lens equation can easily be solved by using the reciprocal button (1/x) on most calculators: 11 1. pqf Finding . Power of a Lens. f: P q1/x + 1/x = 1/x Same with reverse notation calculators might be: Finding f: P q1/x. The reciprocal of the focal length of a lens, when it is measured in metre, is called power of a lens. As a demonstration of the effectiveness of the lens equation and magnification equation, consider the following sample problem and its solution. 1.5 Thin Lenses Formula and Lens maker’s Equation {Considering the ray diagram of refraction for 2 spherical surfaces as shown in figure below. Or should it be a plus sign for mirrors and minus for lenses? Derive the formula where s = distance of object from lens s' = distance of image from lens f = focal length of the lens. Determine the image distance and the image size. 1 1 1 p q f + = 2.1.1 Or is it? • Describe the relationship between collimated light and the focal points of a thin lens. 1/x + 1/x Possible sequence for finding fon linear calculators: Be careful with substitution of signed numbers!Be careful with substitution of signed numbers! • Describe the f-number and numerical aperture for a lens and explain how they control image brightness. Should that not be a minus sign on the left hand side? • Use ray-tracing techniques to locate images formed by thin lenses. Writing the lens equation in terms of the object and image distances, 1 o + 1 i = 1 f. (8) But o1 and i2 are the object and image distances of the whole lens, so o1 = o and i2 = i. Derivation of Lensmaker’s formula. Derivation. Second Formula for Magnification There is another formula of magnification Note : - If magnification (m) is positive , It means image formed is virtual and erect If magnification (m) is negative, It means image formed is real and inverted Questions Example 10.1 - A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. Power of a lens, (P)= 1/f(metre) Its unit is diopter (D). Enter. Sample Problem #1 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a double convex lens having a focal length of 15.2 cm. Lens Maker’s formula 1/f=(μ – 1) (1/R 1 – 1/R 2) where, μ = refractive index of the material of the lens and R 1 and R 2 are radii of curvature of the lens. (“ More for a Mirror; Less for a Lens.”?) The equation that relates object distance p, image distance q and focal length f is . Thus, 1 f = (n −1) 1 R1 + 1 R2 , (9) which is the lensmaker’s formula. Practice Problems. • Use the lensmaker’s equation to determine the focal length of a thin lens.
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