With a concave mirror, an object is placed at a distance x1 from the principal focus, on the principal axis. The image is formed at a distance x2 from the principal focus. The focal length of the mirror is

Question

With a concave mirror, an object is placed at a distance x1 from the principal focus, on the principal axis. The image is formed at a distance x2 from the principal focus. The focal length of the mirror is (A) x1 x2 (B) (x1+x2) / 2 (C) √x1 / x2 (D) √x1 x2

Tardigrade Admin · Accepted Answer

(1/u)+(1/v)=(1/f) (1/f-x1)+(1/f-x2)=(1/f) or (f-x2+f-x1/(f-x1)(f-x2))=(1/f) or f2-f x2-f x1+x1 x2=2 f2-f(x1+x2) or f2=x1 x2 or f=√x1 x2 This is Newton's mirror formula.

Q. With a concave mirror, an object is placed at a distance $x_{1}$ from the principal focus, on the principal axis. The image is formed at a distance $x_{2}$ from the principal focus. The focal length of the mirror is

$x_{1} x_{2}$

$(x_{1} + x_{2}) /2$

$x_{1} / x_{2}$

$x_{1} x_{2}$

Q. With a concave mirror, an object is placed at a distance x1​ from the principal focus, on the principal axis. The image is formed at a distance x2​ from the principal focus. The focal length of the mirror is

x1​x2​

(x1​+x2​)/2

x1​/x2​​

x1​x2​​

u1​+v1​=f1​ f−x1​1​+f−x2​1​=f1​ or (f−x1​)(f−x2​)f−x2​+f−x1​​=f1​ or f2−fx2​−fx1​+x1​x2​=2f2−f(x1​+x2​) or f2=x1​x2​ or f=x1​x2​​ This is Newton's mirror formula.

Q. With a concave mirror, an object is placed at a distance $x_{1}$ from the principal focus, on the principal axis. The image is formed at a distance $x_{2}$ from the principal focus. The focal length of the mirror is

$x_{1} x_{2}$

$(x_{1} + x_{2}) /2$

$x_{1} / x_{2}$

$x_{1} x_{2}$