IIT JEE , AIEEE Forum - Physics , Optics

rtiit

f is the focal lenght of convex mirror
If images of O formed by both the mirrors coincide then find magnitude of f..

rtiit

ne replys plz

spideyunlimited

OK HERE GOES

For first mirror, image will be formed at distance x behind it :).

Now this is a distance y - x from the convex mirror.

This must b the image distance from it also :)

Also... object distance for it is x + y.

So for convex mirror :

u = - (y-x)

v = -(x+y)

1/f = 1/u + 1/v

1/f = -1/y-x - 1/x+y

1/f = [-(x+y) - (y-x) ] / y² - x²

1/f = -2y / y² - x²

1/f = 2y / x² - y²

f = x² - y² / 2y

rtiit

how did u get it??

elastiboysai

I see a flaw in the question!

Image can be formed by plane mirror under the condition x<y.

Bt den img by mirror will be on d oder side,

now contrarily,

if x>y den only 1 image will b formed as lite rays frm d mirror cant form an indepdt img??

Correct me if im wrong

computer001

i dun understand elasti

i think x<y thts all..
as only then the 1st img will be formed in front of mirror..

computer001

i think ans shud be (y-x)/2
spidey r u sure of urs??

rtiit

answer given here is (x^2-y^2)/2y

m not gettin it

computer001

EDITED

spideyunlimited

FELLOW INDIANS :D
look above :D

rtiit

great gaurav

spideyunlimited

also@computer :)
if the 2 mirrors are considered at the same time, the convex mirror cant form any image as no light ray will actually fall on it. the image just appears inside or behind the plane mirror and a virtual image (which is formed when light rays apear to meet but dont actually meet :) )

so we have to consider the two mirrors' cases separately and equate position of image :)

computer001

spidey all tht is ok...tht is quite direct but the pt is how does the object directly act as a source to the conv mirror...??

soln is fine but pl explain the logic

EDITED:
gave a silly thot which has been removed..corrected by spidey

computer001

c buddy the question says the 2 images COINCIDE which is possible only if both mirrors are used @ the same time

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