Find the distance and the nature of an object of size 5cm placed at a distance of 8cm in front of concave mirror who's radius of curvature is 20cm.
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Given :
- Object Height (ho) = 5 cm
- Image Distance (u) = - 20 cm
- Radius of curvature (R) = 30 cm
- Convex Mirror
To Find :
Position, nature and size of the image
Solution :
As we know that,
➠ R = 2f
⇒30 = 2f
⇒f = 30/2
⇒f = 15
Focal length of the mirror is 15 cm
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Now, use mirror formula :
➠1/f = 1/v + 1/u
⇒1/15 = 1/v + (-1/20)
⇒1/15 = 1/v - 1/20
⇒1/v = 1/15 + 1/20
⇒1/v = 4 + 3/60
⇒1/v = 7/60
⇒v = 60/7
⇒v = 8.57
Image position is 8.57 cm from mirror
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Size and nature of Image can be find out using formula of Power of mirror,
➠ m = -v/u = h'/ho
⇒-8.57/-20 = ho/5
⇒ho = 0.437 * 5
⇒ ho = 2.185
∴ Height of object is 2.185 cm and nature is Virtual and erect
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