Giving an optical system compose of two lens system. Lens 1 focal length = 10-cm

Question

Giving an optical system compose of two lens system. Lens 1 focal length = 10-cm, Lens 2 focal length = 5-cm. The distance between the two lenses L = 50-cm. An object is 30 meter away from Lens 1, with height of 10-cm (a) Setup the equation, that solve the image location and the magnification, at each lens (b) Solve the image location, magnification, and height at each lens? (c) If you want the object to have a final magnification of 1, m = 1. What will object location, and the L distance between lenses have to be.? (d) If the object is 10000 meters away what will the image distance be for lens 1?

Explanation / Answer

(a) Using lens euation : 1/u + 1/v = 1/f.........(i)

where u = object distance v= image distance f = focal length

For connvex lens as shown , f = +ve value

For lens-1 , u = -30cm f = 10cm , so from (i) v can be found as -1/30 + 1/v = 1/10

so , v=+7.5cm (Real image)

magnification, m = -v/u = -7.5/-30=1/4

Similarly, for lens 2, image created by first lens acts as image to the lens 2.....

so, u=-7.5cm, f=+5cm using (i) gives v = +3cm

magnification, m = -3/-7.5 = 0.4

(b) w e have found the magniffication and image loctaion in part (a) which can be used to find image heigth as

Magnification, m=image heigth / object heigth

For lens 1 , 1/4 = hi / 10 so hi = +2.5cm (Upward straight Image)

For lens 2, 0.4 = h'i / 2.5 so   h'i = 1cm

(c) For m = 1 , object location is: -v / u = 1

so for lens 1 v = -u = +30 cm

(d) For an object to 10000m away as before using (i)...

v is found as v = 0.099m = 9.9 cm

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