Question

when a concave mirror is placed facing the sun, the sun's rays converge to a point 10cm from the mirror .now, if you place 2 cm long candles flame in 20 cm Away on the principal axis of the mirror, where would you place a screen to obtain the image of candle? what would see the size of the image?

Answer 1

we know when light ray comes from infinite distance ( or very far distance ) strike into mirror then they converge to a point known as focus. and distance of focus to pole of mirror is known as focal length .
hence ,
focal length of mirror = -10 cm { focal length negative due to concave mirror }

now,
use mirror formula,
1/v + 1/u =1/f
1/v + 1/(-20) = 1/(-10)

1/v = 1/20 - 1/10
v = -20 cm
hence position of image is also 20cm in side of object .
also ,
magnification = -v/u
= -(-20)/(-20)
= -1
hence,
magnification = -1
this implies that size of object is equal to size of image . and negative sign of magnification indicate image formed real and inverted

Answer 2

Given:
Sunrays from Sun strike concave mirror and after reflection converges at a point Focus (F) on the principal axis.
So, focal length =f= -10cm.( by sign convention).
U= -20cm.
Mirror formula:
1/f=1/u+ 1/ v
1/v= 1/f-1/u
=1/-10 +1/20
=-2+1/20
V=-20cm.
Hence screen should be placed at a distance of 20cm from the mirror.
TO FIND NATURE OF IMAGE:
m=-v/u= hi/ho
hi=-(-20)/-20 X 2
hi=-2cm
SO, m = hi/ ho
m=-2/2
m=-1
Magnification is negative, THIS IMPLIES THAT image formed is real and inverted
m=1 IMPLIES that size of object equals to size of image.