An object is placed at a distance of 30cm from a convex mirror, the magnification produced is 1/2. Where should the object be placed to get a magnification of 1/3.
Answers
ANSWER :
MIRROR : It is a shiny polished glass which reflects most of the rays of light falling upon it.
TYPES OF IMAGE FORMED BY IT : Real and Virtual.
TYPES OF MIRROR : Plain mirror and Spherical mirror.
SPHERICAL MIRROR having 2 types of MIRRORS : Concave and Convex mirrors.
CONVEX MIRROR :
- Spherical mirror with reflecting surface curved outwards is called convex mirror.
- Used as rear view mirror in vehicles because it gives erect image. It helps the driver to view large area.
SIGN CONVENTIONS FOR CONVEX MIRROR :
1. Object distance " u " = ₋ve
2. Image distance " v " = always + ve
3. Focal Length " f " = + ve
4. Height of virtual image = +ve
5. Height of real image = ₋ve
⇒
Given in the question that :
( object distance ) u = ₋ 30cm
( Magnification produced ) m = 1/2
Using the formula, m = ₋v/u ( For a convex spherical mirror )
∴ 1/2 = ₋v/₋30
v = + 15cm.
Now, Using mirror formula, 1/f = 1/v + 1/u
1/f = 1/15 + 1/₋ 30 = 1/30
∴ f = + 30cm
Again, m' = ₋ v'/u'
1/3 = ₋ v'/u'
v' = ₋ u'/3
Using again the mirror formula, 1/f = 1/v' + 1/u'
1/30 = ₋ 3/u' + 1/u' = ₋2/u'
→ u' = ₋ 60cm
Hence, the object should be placed at a distance of 60cm in front of a convex to get the magnification of 1/3.
Answer:
Explanation:
Given :-
u = 30 cm
m = 1/2
Solution :-
Using, m = - v/u, we get (For Convex Spherical mirror)
⇒ 1/2 = - v/- 30
v = + 15 cm
Using, 1/f = 1/v + 1/u, we get
⇒ 1/f = 1/15 + 1/- 30
⇒ 1/f = 2 - 1/30
⇒ 1/f = 1/30
⇒ f = + 30 cm
Again, m' = v'/u'
⇒ v' = - u'/3
Using again, 1/f = 1/v' + 1/u'
⇒ 1/30 = -3/u' + 1/u'
⇒ 1/30 = - 2/u'
⇒ u = 30 × (- 2)
⇒ u = - 60 cm
Hence, the object be placed at a distance of - 60 cm to get a magnification of 1/3.