The radius of curvature of a mirror is 86 an. A diamond ring is placed in front

Question

The radius of curvature of a mirror is 86 an. A diamond ring is placed in front of this mirror. The image is three times the size of the ring. ) Is the mirror concave or convex, or is elther type possible? concave convex either type is possible (i) How many places are there in front of a concave mirror where the ring can be placed and produce an image three times the size of the object? o 3 (ii) What are the possible values for the magnification of the image of the ring? (Enter your answers from to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) smallest none Find the possible object distances of the ring. (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) 57.33 28 67 cm cm e prt sc deleteh f11 f9 110 backspacs 8 0

Explanation / Answer

To find the possible object distances of the ring

Given R = 86 cm and magnification of the image of the ring, m = -3

and second case the image is upright, so the magnification is m = +3

R = 2f

f = 86/2 = 43 cm

On solving magnification equation we have v = -mu; substituting this expression for v in mirror equation, we get

(1/u)+[1/(-mu)]=(1/f)

u = [f(m-1)]/m

Applying this result, we obtain

m = -3, u = [f(m-1)]/m=[(-43)(-3-1)]/(-3)=-57.33 cm

m = +3, u = [f(m-1)]/m=[(-43)(+3-1)]/(-3)=+28.66 cm

Answers are

None

-57.33 cm

+28.66 cm

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