Determine the image distance and image height for a 5.0-cm tall object placed 48.0-cm from a converging lens having a focal length of 24.0.
Answers
Answer:
Given that,an object placed 45.0 cm from a concave mirror having the focal length 15.0 cm
and height of image is 5.0 cm
we have to find the image distance (v) from the mirror and height of the image (hi).
From above data we have,focal length (f) of concave mirror is −15 cm, object distance (u) is −45 cm height of image (hi) is 5 cm.
Now, using mirror formula:
f
1
=
v
1
+
u
1
where f is focal length, v is image distance from the mirror and u is object distance from the mirror (concave).
Substitute the known values in the above formula to find the value of 'v' i.e. image distance from the mirror.
(−15)
1
=
v
1
+
(−45)
1
15
−1
=
v
1
−
45
1
15
−1
+
45
1
=
v
1
45
(−3+1)
=
v
1
45
−2
=
v
1
22.5=v
Therefore, the image distance from the concave mirror is −22.5 cm
Now,
m=
u
−v
=
ho
hi
substitute the values,
−45
−(−22.5)
=
5
hi
−0.5=
5
hi
−2.5=hi
Therefore, the height of the image is −2.5 cm