Question

A 5-cm-high peg is placed in front of a concave mirror with a radius of curvature of 20 cm.

USE THE ABOVE INFORMATION TO ANSWER QUESTION 3 TO 6
The focal length of a convex mirror is 10 cm and the object distance is 20
Determine the image height if the peg place at the object distance of 5 cm from the concave mirror
4. Determine the image height if the peg place at the object distance of 15 cm from the concave mirror
5. Determine the image height if the peg place at the object distance of 20 cm from the concave mirror
6. Determine the image height if the peg place at the object distance of 30 cm from the concave mirror

Answer 1

Step-by-step explanation:

Using the magnification formula.

Magnification = Image distance(v)/object distance(u) = Image Height(H1)/Object Height(H2)

M = v/u = H1/H2

v/u = H1/H2...1

3) Given the radius of curvature of the concave lens R = 20cm

Focal length F = R/2

f = 20/2

f = 10cm

Object distance u = 5cm

Object height H2= 5cm

To get the image distance v, we will use the mirror formula

1/f = 1/u+1/v

1/v = 1/10-1/5

1/v = (1-2)/10

1/v =-1/10

v = -10cm

Using the magnification formula

(10)/5 = H1/5

10 = H1

H1 = 10cm

Image height of the peg is 10cm

4) If u = 15cm

1/v = 1/f-1/u

1/v = 1/10-1/15

1/v = 3-2/30

1/v = 1/30

v = 30cm

30/15 = H1/5

15H1 = 150

H1/= 10cm

5) if u = 20cm

1/v = 1/f-1/u

1/v = 1/10-1/20

1/v = 2-1/20

1/v = 1/20

v = 20cm

20/20 = H1/5

20H1 = 100

H1 = 5cm

6) If u = 30cm

1/v = 1/f-1/u

1/v = 1/10-1/30

1/v = 3-1/30

1/v = 2/30

v = 30/2 cm

v =>15cm

15/30 = Hi/5

30H1 = 75

H1 = 75/30

H1 = 2.5cm