Question

3.) A circular object is placed to the left of a mirror that is polished on both sides: the concave side has focal length fconcave = +18cm and the convex side has length fconvex = −18cm. The distance between object and the mirror is not known. You can see a circular image on a screen that is placed to the left of the object.

a) What can you tell about the image formation based on the information given so far? [Open-ended question]

b) The distance between the object and the screen is 5.2 cm. Find the object and image distances!

c) The circle on the screen has diameter 2.4 cm. What is the diameter of the circular object?

Answer 1

a) the concave side is facing the object as image is formed on the same side as the object and so the image is real and inverted.

b) The mirror formula is :

1/di = 1/f – 1/do

di is image distance

do is object distance

f is focal length.

The distance between object and screen is 5.2 cm that means object is placed between the focal point and radius of curvature than only the real image is formed by the concave mirror beyond the object.

do has to be les than Radius of curvature that is 2*f =36cm and more than focal length =18cm hence the positive sign in the solution is chosen.

f = +18cm

di = do+5.2

1/18 = 1/do + 1/(do+5.2)

I have multiplied f value as 18 in the picture above.

hence do = 33.59cm so round off the distance of object to be 33.6cm

hence image distance = 33.6+5.2= 38.8cm

c) magnification = -di/do = -38.8/33.6 = -1.15

magnification = hi/ho

hi = image size

ho = object size

size can be directly taken as diameter since even if we calculate area or circumference, for magnification ratio is needed and the constants will cancel leaving behind diameter ratios.

hi = 2.4cm

ho = - 2.4/1.15 = -2.08 cm

negative sign implies the image is inverted and since magnification is more than 1 in magnitude, the image is enlarged.

all this matches with our assumptions made this far.

Do like if this helps!