Question

AN OBJECT AND ITS IMAGE BY A MIRROR OF LENGTH F HAVE A DISTANCE FROM FROM THE FOCUS IN THE RATIO 1:4,THE OBJECT DISTANCE IS

Answer 1

Answer:

3f/2

Explanation:

[u=object distance

f=focal length

F=focus]

for a spherical mirror,

m=f/p ---------1  [where p is distance of object from F]

m=p/f ---------2  [where p is the distance of the image from F]

given,

distance of object : distance of image = 1 : 4

let us assume distance of object from F is x

u=f+x ------- 3

p : p = 1 : 4

p=x , p=4x

2 => m= f/p= f/x ----------2'

3 => m= p/f= 4x/f -----------3'

equating 2' and 3'

m= m

f/x= 4x/f

f^2= 4(x^2)

x^2= f^2/4

x= f/2 -----------4

putting 4 in 1

u= f+x

u= f+(f/2)

u= 3f/2

Hope this helps!