Sign Convention for Spherical Lens

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CHAPTER TEN - LIGHT - REFLECTION AND REFRACTION

 

1.20 Sign Convention for Spherical Lens                                                                                          

For solving problems related to lens, we have to measure all the distances from optical centre, to understand the direction of measurement we takes some conventions is called sign convention.

Assuming origin of Cartesian coordinate system is concentric with optical centre of lens and the object is placed at left side of lens so that light ray fall on lens from left-hand side. Then following conventions are

1. All the distances are measured from optical centre.
2. All the distance measured right sides of the optical centre are taken as positive.
3. All the distance measured left sides of the optical centre are taken as negative.
4. All the distance measured above the optical centre (principal axis) is taken as positive.
5. All the distance measured below the optical centre (principal axis) is taken as negative.

 

Hint: If we move from optical centre/origin, along positive axis, distances are positive and along negative axis, distances are negative.

 

 

1.21 Lens Formula and Magnification (Derivation not required)                                          

 

Lens Formula: The relation between position of object, position of image and focal length of lens

Distance of object from the optical centre is called Position of object (u)

Distance of image from the optical centre is called Position of image (v)

Perpendicular distance of object’s head from the optical centre/principal axis is called Height of object (ho)

Perpendicular distance of image’s head from the optical centre/principal axis is called Height of image (hi)

 

The relation between position of object, position of image and focal length of lens is called Lens formula

 

 1             1             1

__     =    ___    -     ___

          f             v             u

 

Hint: If we replace u with –u in mirror formula it becomes lens formula

Magnification:  Ratio of height of image to height of object is called Magnification of lens

 

It tells that our lens made image how many times bigger or smaller of the given object. If magnification of a given 2 it means image will be twice taller of object.

Hint: If we replace u with –u in mirror magnification it becomes lens magnification.

Magnification can be Negative or Positive.

 

For real image: u is –ve and v is also +ve by putting value in above formula we have, m = -ve

or

ho is +ve and hi is –ve by putting value in above formula we have, m = -ve

 

For virtual image: u is –ve and v is -ve by putting value in above formula we have, m = +ve

or

ho is +ve and hi is also +ve by putting value in above formula we have, m = +ve

 

From the above discussion, magnification of real image is always –ve and of virtual image is always +ve

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