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Question

Go to http://phet.colorado.edu/en/simulation/geometric-optics

Click the Run Now button to start the web simulations, set the radius of curvature to 1.2 m, the refractive index to 1.75 and the diameter to 1.2 m

Bring the flashlight closer to the lens than the focal point.
a) What happens to the rays? Is an image formed? If so, describe this image.
b) Where do you need to put the flashlight to get a virtual image that is three times the focal length distant from the lens? Draw the rays for this configuration.
c) Where would you need to put your eye to see the image? Draw this on your diagram.
d) What are p, q and the magnification for this setup?

Explanation / Answer

a.) The rays scatter and do not converge. A real image is not formed however a virtual image is formed. b.) Use the thin lense equaion: 1/S_1 + 1/S_2 = 1/f where S_1 is the object distance, S_2 is the image distance (virtual if negative), and f is the focal length. You need to know at what object distnce (S_1) will the image distance (S_2) be equal to 3 times the focal lenght (3*f) and it should be negative since the image needs to be a virtual image (-3*f) 1/S_1 - 1/3f = 1/f 1/S_1 = 1/f + 1/3f 1/S_1 = 4/3*f S_1 = .75 *f So the object needs to be .75 times the focal length from the lesne. c.) You would need to put your eye on the back side of the lense, oppsite side that the image is on. See here, the last ray diagram: http://homepage.mac.com/cbakken/obookshelf/cvvirtual.html d.) p and q are the same as my S_1 and S_2. If you want to know the actual distances you need to know the focal length, this is obtained using the thin lense aproximation and the lense makers equation: 1/f = (n-1) * [ (1/R1) - (1/R2) ] in the case you gave, n = 1.75, R1 =1.2, R2 = -1.2 The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The sign convention used to represent this varies, but in this article if R1 is positive the first surface is convex, and if R1 is negative the surface is concave. The signs are reversed for the back surface of the lens: if R2 is positive the surface is concave, and if R2 is negative the surface is convex. 1/f = (1.75 - 1) * [ (1/1.2) + (1/1.2)] 1/f = 1.25 f = .8m p = .6m q = -2.4m M = -q/p M = 4 Hope this helps!

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