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Question
List the new Cartesian sign convention for reflection of light by spherical mirror. Draw a diagram and apply these conventions for calculating the focal length and nature of spherical mirror which forms a 1/3 times magnified virtual image of an object placed 18 cm in front of it.
Solution
New Cartesian Sign Conventions for reflection of light by spherical mirrors are given below:
1. The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
2. All distances parallel to the principal axis are measured from the pole of the mirror.
3. All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along − x-axis) are taken as negative.
4. Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
5. Distances measured perpendicular to and below the principal axis (along −y-axis) are taken as negative.
`m=1/3`
u = -18 cm
f = ?
v = ?
`m=-v/u=1/3`
`=>v=-u/3=-((-18))/3=6` cm
Now, according to mirror formula
`1/v+1/u=1/f`
`1/6+1/((-18))=1/f`
`1/f=(3-1)/18`
`1/f=2/18`
`f = 9` cm
Since the focal length is positive so, it is a convex mirror.
Ray diagram:
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RELATED QUESTIONS
If R is the radius of curvature of a spherical mirror and f is its focal length, then:
(a) R = `f`
(b) R =` 2f`
(c) R = `f/2`
(d) R = `3f`
The focal length of a spherical mirror of radius of curvature 30 cm is:
(a) 10 cm
(b) 15 cm
(c) 20 cm
(d) 30 cm
List the sign conventions for reflection of light by spherical mirrors. Draw a diagram and apply these conventions in the determination of focal length of a spherical mirror which forms a three times magnified real image of an object placed 16 cm in front of it.
What sign conventions are used for reflection from a spherical mirror?
According to sign convention the distance of the object ______.
According to sign convention the distance of the image ______.
The variation of image distance (v) with object distance (u) for a convex lens is given in the following observation table. Analyse it and answer the questions that follow:
Sr. No. | Object distance (u) cm | image distance (v) cm |
1 | -150 | +30 |
2 | -75 | +37.5 |
3 | -50 | +50 |
4 | -37.5 | +75 |
5 | -30 | +150 |
6 | -15 | +37.5 |
- Without calculation, find the focal length of the convex lens. Justify your answer.
- Which observation is not correct? Why? Draw ray diagram to find the position of the image formed for this position of the object.
- Find the approximate value of magnification for u = – 30 cm.