An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the image formed is d 2 from C, the radius of curvature of this mirror is :

Question

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the image formed is d 2 from C, the radius of curvature of this mirror is : (A) (2 d 1 d 2/ d 1- d 2) (B) (2 d 1 d 2/ d 1+ d 2) (C) ( d 1 d 2/ d 1+ d 2) (D) ( d 1 d 2/ d 1- d 2)

Tardigrade Admin · Accepted Answer

Using Newton"s formula ( f + d 1)( f - d 2)= f 2 f 2+ fd 1- fd 2- d 1 d 2= f 2 f =( d 1 d 2/ d 1- d 2) ∴ R =(2 d 1 d 2/ d 1- d 2)

Q. An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is $d_{1}$ from $C$ and the distance of the image formed is $d_{2}$ from $C$ , the radius of curvature of this mirror is :

$\frac{2 d _{1} d _{2}}{d _{1} - d _{2}}$

$\frac{2 d _{1} d _{2}}{d _{1} + d _{2}}$

$\frac{d _{1} d _{2}}{d _{1} + d _{2}}$

$\frac{d _{1} d _{2}}{d _{1} - d _{2}}$

Using Newton"s formula
$(f + d_{1}) (f - d_{2}) = f^{2}$
$f^{2} + f d_{1} - f d_{2} - d_{1} d_{2} = f^{2}$
$f = \frac{d _{1} d _{2}}{d _{1} - d _{2}}$
$∴ R = \frac{2 d _{1} d _{2}}{d _{1} - d _{2}}$

Q. An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1​ from C and the distance of the image formed is d2​ from C, the radius of curvature of this mirror is :

d1​−d2​2d1​d2​​

d1​+d2​2d1​d2​​

d1​+d2​d1​d2​​

d1​−d2​d1​d2​​