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Unformatted text preview: Quiz 2 DL Sec Last 6 digits of student ID: Grading: Name: First three letters of your family name 1. You are going to and take a photo of the physics building to post on your blog about how much you like physics. The physics building is approximately 25 meters tall. We stand about 200 meters away (that is, we are standing on the path next to the bike barn). The camera that we are going to use is just a box with a piece of ﬁlm on it. The box is 12mm deep, but the lens protrudes a further distance (see diagram). We can adjust to get the building focused on the ﬁlm. Show working for all parts! 12mm 25 m 36mm 200 m f The ﬁlm is 36 mm tall, and the image of the building is shown on it. Note the image takes up the entire lower half of the ﬁlm! We are taking the physics building to be 200m from the from the lens. (a) What is the magniﬁcation of the lens? Show working. (b) What does the distance have to be for this image to be in focus? (c) What focal length lens do you have to use? 2. As we have discussed in lecture, there are three ways for light to not travel in a straight line. Mirrors and lenses work by reﬂection and refraction, but the third way is diﬀraction and happens λ whenever light passes through an opening. The angle of spread is given by θ = D where λ is the wavelength of the wave, and D is the size of the hole the light is going through. As we noted in lecture if D is much bigger than the wavelength λ then θ is small so the light travels “almost” straight. h λ = 555 × 10−9 m 25 mm
Shown here is a picture of an eye a ray coming into the center of it. Diﬀraction spreads the light out an angle θ on both sides of the central ray. (a) If the pupil (i.e. lens) in the eye is 2 cm high (i.e. D = 2 cm) what is the angle of spreading θ caused by diﬀraction? Note the formula above gives an answer in radians. (b) Ignoring the curvature of the retina, what distance h will be covered by light from this central ray? Hint: you can you right angled triangles. (c) We learnt in DL that we have approximately 300 receptors per mm in our eye. Eventually diﬀraction spreads the light so much that we would not get better “resolution” from an increased number of photoreceptors. How closely can we space the photoreceptors so that the light from the single ray in this example only lands on one of them? ...
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- Fall '08