An object is placed beyond the centre of curv | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For a spherical mirror,Newton's formula relates the distances of the object and image from the focus $F$. Let $x_{1}$ and $x_{2}$ be the distances

Vedclass · Accepted Answer

$\frac{2 d_{1} d_{2}}{d_{1}-d_{2}}$

Vedclass · Answer

(A) For a spherical mirror,Newton's formula relates the distances of the object and image from the focus $F$. Let $x_{1}$ and $x_{2}$ be the distances of the object and image from the focus,respectively. The formula is $x_{1} x_{2} = f^{2}$.In this problem,the distances are measured from the centre of curvature $C$. The distance of the focus $F$ from $C$ is the focal length $f$. Thus,the distance of the object from the focus is $x_{1} = d_{1} + f$,and the distance of the image from the focus is $x_{2} = f - d_{2}$.Substituting these into Newton's formula: $(f + d_{1})(f - d_{2}) = f^{2}$.Expanding the equation: $f^{2} - f d_{2} + f d_{1} - d_{1} d_{2} = f^{2}$.Simplifying: $f(d_{1} - d_{2}) = d_{1} d_{2}$.Therefore,the focal length is $f = \frac{d_{1} d_{2}}{d_{1} - d_{2}}$.The radius of curvature $R$ is given by $R = 2f$.Hence,$R = \frac{2 d_{1} d_{2}}{d_{1} - d_{2}}$.

An object is placed beyond the centre of curvature $C$ of a 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

Similar Questions

For a point object,which of the following always produces a virtual image in air?

Assertion : The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason : Laws of reflection are strictly valid for plane surfaces,but not for large spherical surfaces.

$STATEMENT-1$: The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. because
$STATEMENT-2$: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

$A$ square cardboard of side $3\, cm$ is placed $25\, cm$ from a concave mirror of focal length $10\, cm$. What is the area enclosed by the image of the cardboard? (The plane of the cardboard is perpendicular to the principal axis.)

$A$ candle flame of $3\, cm$ is placed at $3\, m$ from a wall. $A$ concave mirror is kept at a distance $x$ from the wall in such a way that the image of the flame on the wall is $9\, cm$. Then $x$ is......$cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module