determine the image distance and age height fo a 5.5cm tall obhect placed 54.0 from a converging lens having a focal length of 20.0cm
Answers
Answer:
Image distance(v) = 14.5 cm
Height(hi) = 1.47 cm
Explanation:
Given that, an object placed 54 cm from a convex mirror having the focal length of 20.0 cm and height of image is 5.5 cm.
We have to find the image distance (v) from the mirror and height of the image (hi).
Form above data we have, focal length (f) of concave mirror is 20 cm, object distance (u) is -54 cm and height of image (hi) is 5.5 cm.
Now, Using Mirror Formula:
1/f = 1/v + 1/u
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.
1/20 = 1/v + 1/(-54)
1/20 = 1/v - 1/54
1/20 + 1/54 = 1/v
0.069= 1/v
v= 14.49
Therefore, the image distance from the convex mirror is 14.5 cm.
Now,
m = -v/u = hi/ho
Substitute the values,
-(14.5)/(-54) = hi/5.5
0.268 = hi/5.5
1.47 = hi
Therefore, the height of the image is 1.47 cm.