Lenses may be simple ones with two spherical curved surfaces on a piece of trans

Question

Lenses may be simple ones with two spherical curved surfaces on a piece of transparent material like glass or plastic, or much more complex and compounded of different elements each with sometimes a different material. The surfaces do not have to be spherical, and manufacturing techniques today allow combining these "aspheric" lenses in designs that produce exquisite detail in an image. Your cell phone camera lens is an example, as are the lenses of a larger digital or photographic camera. This week's problem is chosen to get to the basics of lenses and how they work because they are the most common essential component of optical instruments. Starting with Snell's law, you can show that a lens has a property called a "focal length" such that 1/f= 1/p + 1/q where p is the distance to the object in front of the lens, and (q) is the distance from the lens to the image it forms. This applies to a lens so thin that the thickness of the glass is small compared to these distances. Light from infinity must form an image at q = f Written this way, there is a convention to measure the distance to the object as positive to the left of the lens, and the distance to the image as positive to the right of the lens. 1. Where does light coming from a distance f in front of the lens form an image? Explain. 2. If I want a lens to be halfway between an object and a screen where the image forms, what is the focal length of the lens? You may answer generally, or if you prefer a specific case let the object and the screen be 10 cm apart. 3. The focal length of a thin lens is given by the "lens maker's equation" 1/f= (n-1)(1/A-1/R2)It

Explanation / Answer

1. given p = f

   1/f = 1/f +1/q .......1/q = 1f - 1/f = 0

    1/q = 0

q = infinity     means image forms at infinite distance

2. means p = q

1/f = 1/p + 1/p = 2/p

f = p/2

given p+q =10cm     so p =q = 5cm

f = p/2 = 2.5cm

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