An object 5 cm high is held 25 cm away from a converging lens of radius of curvature 20cm.
Find the position size and nature of image formed.Also draw the ray diagram.
Answers
GivEn :
- The height of object, h = 5cm
- Position of object, u = - 25cm
- Radius of curvature, R = 20 cm
To find :
Position size and nature of image formed. Also draw the ray diagram.
SolutioN :
I'm order to find the position size and nature of image formed we'll have to calculate the focal length of the lens as well as the image distance.
We know that,
⇒ Focal length = R/2
⇒ Focal length = 20/2
⇒ Focal length = 10 cm
To calculate the image distance we've to use the lens formula.
By using lens formula :
⇒ 1/v - 1/u = 1/f
Substituting the values,
⇒ 1/v + 1/25 = 1/10
⇒ 1/v = 1/10 - 1/25
⇒ 1/v = (5 - 2)/50
⇒ 1/v = 3/50
⇒ v = 50/3
⇒ v = 16.66 cm
∴ Distance of the image is 16.66 cm on the opposite side of the converging lens.
Also, we can calculate the height of the image by calculating the Magnification.
⇒ Magnification = v/u
⇒ Magnification = 16.66/-25
⇒ Magnification = -0.66
Now,
⇒ Magnification = height of image/height of object
⇒ Magnification = hi/ho
⇒ -0.66 = hi / 5 cm
⇒ hi = -3.3 cm
NOTE : -ve sign of the height of image predicts that the image formed is inverted.
Also, image is formed at 16.66 cm on the opposite side of the converging lens.
Image formed real & inverted with - 3.3 cm at the opposite side of the converging lens.
