IIT JEE , AIEEE Forum - Physics , Optics - A beam of light converges to a point P. A lens is ............

sneha.bagri

A beam of light converges to a point P. A lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is a convex lens of f=20cm? Please explain sign conventions for this sum.

akhil_o

1/v=1/u+1/f

u,f are neg

hence

1/v=1/.2 -1/.12

1/v= -3.33

v=-30 cm

raulrag009

i think

u= -12

but

f=+20

hence 1/v-1/u=1/f

1/v+1/12=1/20

v=-30cm

sneha.bagri

but i have seen in some books like NCERT(unsolved) , pradeeps (solved) etc u is taken positive................

ramyani

There r 2 sign conventions.

1. R P ( real is +ve ) sign convention :

this tells anything that is normal is +ve ( my language ).

for a mirror, a ray falling on it should and does come back towards the object. So that side is real.

for a lens, a ray falling on it should cross and so other side is real.

2. co-ordinate sign convention :

just assume that the optical center of the lens or mirror as origin and imagine X and Y axis. +ve or -ve sign accordingly.

co-ordinate sign convention is more widely used.

SIGN CONVENTION:

The pole is taken as the origin and rest of the distances are calculated according to it. Thus

? All the distances on the right side are +ve. Thus focus is +ve in case of convex mirror while it is -ve in case of concave mirror.

? Above rule holds, if incident ray is travelling from left to right else directions just reverses.

? Distances measured above principal axis are taken to be positive while distances measured below principal axis are taken to be negative.

notations used:-

u:

Distance of the object from pole of spherical mirror.

v:

distance of the image from the pole of the spherical mirror.

f:

focal length of the spherical mirror.

R:

Radius of curvature of the spherical mirror.

? All the symbols used are assigned values with proper sign convention. i.e. for concave mirror f is always -ve and so on.

( source : http://www.goiit.com/chapters/tutorial/physics/geometric-optics-2.htm

spideyunlimited

yes 'u' will be +ve here, as the image on point P acts as as an object for our purpose. and focal length will become negative because for this 'object' (which is actually an image), the rays passing through lens will converge at other side.

now 1/f = 1/v - 1/u
1/-20 = 1/v - 1/12
1/v = -1/20 + 1/12
1/v = -3 + 5 / 60
v = 60 / 2 = 30 cm approx.
same side as P.

sneha.bagri

in NCERT f and u both are taken as positive and ans is 7.5.........

sneha.bagri

according to d recent sign convention we have to take d pole as a fixed point of referance and anything which is in d same direction as d incident ray tat is taken as +ve den how come in NCERT its taken +ve 4 both focus and object P ?????? IS IT WRONG????

spideyunlimited

yaar for convex lens, focus and object have opposite signs

jain108

here after placing the lense

u is taken for avirtual object and it is in the direction of rays at pt. p

jain108

answer is correct
=+7.5

sneha.bagri

but as p is d object so we will consider d direction of incident ray according to it na.....???????

ramyani

The light is converging. ok ?

When a convex lens is placed in the path it will converge more.

In that case the point P acts as a virtual object for the lens.

Why virtual object ?

Because the actual object is away and rays coming from that object is focussed at P. It means P is the real image of the object.

But as soon as the lens is placed in between this real image acts as an object for the lens. And hence it acts as an virtual object.

now we follow R P sign Convention. All real things r +ve.

object is virtual here , so - ve

u = - 12 cm

focal length of a convex lens is always on the other side of the lens. Any ray falling on a transparent lens is supposed to pass through it. That is expected or normal .So other side in case of any lens is real side.

In case of a convex lens f falls on the other side. So f is +ve. ( and by the same logic f for a concave lens is --ve )

f = + 20 cm

then, 1/ u + 1/ v = 1/f ( R P sign convention )

gives 1/v = 1/20 + 1/12 = ( 3 + 5 ) / 60 = 8 / 60 = 2 / 15

v = 15/2 = + 7.5 cm

ramyani

But the next part is most important.

It is interpretation of result.

Look the problem is solved in R P sign convention.

the Object distance v is +ve. = > it should be a real image. And as I hav told , for a lens, other side is real.

But here the object itself was virtual. So +ve v means , in this case, virtual image.

So the bottom line is that the image is formed at a distance 7.5 cm from the lens on the same side of P.

Remember, all these +ve and -ve will change if u take co-ordinate sign convention. But the interpretation will give correct result.

And finally , almost all books now follow co-ordinate sign convention. I still stick to R P sign convention as this was what I followed in 10th st. in our board.

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