The distance between a lighted candle and the screen where itsimage is formed is

Question

The distance between a lighted candle and the screen where itsimage is formed is 50cm. The height of the candle is 5 cm andthe height of the image is 3 cm.
a) what is the type of lens in between the object and the image
b) is the image real or virtual
c)what is the focal length of the lens
d)Find the object distance and the image distance

h'= .03m
h=.05 m
|m|=.03/.05
m=.6
.6=-.5/p
p=-.883
i=-.5
-p value indicates back of lens
b) image is virtual
a) convex lens
I am obviously wrong...if someone could show me how to correctly dothe problem or point out my errors I would appreciate it. Thanks

Explanation / Answer

Magnification m = 3cm/5cm = 0.6 now -q/p = 0.6    q = -0.6p Given   p+q = 50cm p-0.6p = 50cm then p = 50cm/0.4 = 125cm and q = -0.6(125cm) = -75cm Now from lens formula   1/f = 1/p + 1/q    f = pq / p+q = (125) (-75) / 125-75 =-187.5 so the lens is concave which gives virtual image

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