(II) The magnification of a convex mirror is +0.65 ×for objects 2.2 m from the mirror. What is t

(II) The magnification of a convex mirror is +0.65 ×for...

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Key Concepts

Mirror Equation

The mirror equation, 1/f = 1/v + 1/u, is a fundamental relation in geometrical optics that links the focal length (f) of a mirror with the object distance (u) and the image distance (v). It is crucial for solving problems related to image formation by mirrors when two of the three quantities are known.

Magnification

Magnification in mirror systems is defined as m = v/u, which indicates the ratio of the image distance to the object distance. It shows how much larger or smaller the image is compared to the object, and its sign reveals whether the image is upright or inverted.

Convex Mirrors and Sign Conventions

Convex mirrors always produce virtual, upright, and diminished images. In these systems, sign conventions are particularly important: the focal length is taken as negative, and the image distance is positive for virtual images. These conventions help accurately apply the mirror equation and interpret the magnification value.

Transcript

00:01 So in this question, our goal is to get the focal length of a mirror and the magnification is 0 .65.

00:12 And the object distance is 2 .2 meters.

00:19 So just like basically every problem we've done, there's two equations, the mirror and the lens equation.

00:25 So 1 over d9 plus 1 over d .o is 2 over r or we can do it as 1 over f because f is 1.

00:34 R over 2.

00:36 And then we also know, like i was saying m, or maybe i didn't say it.

00:43 The other equation is m is negative d .i over do.

00:47 And we also should pay attention to the sign conventions.

00:50 So it's a convex mirror.

00:51 So then this r is going to be, our r should come out a negative number.

00:59 So, yeah, let's go ahead and just do the substitution.

01:04 And we can solve for, oh, sorry, we wanted to actually solve for the focal length.

01:09 So the focal length will be negative if r is negative.

01:12 So this is 1 over f.

01:15 So you can solve from this that f is equal to, oops, i was like really rushing through this problem.

01:24 All right, f is equal to d .i.

01:28 Do over d .i plus d .o.

01:31 That's just combining these denominators properly and then inverting the fraction.

01:37 And then we want to sub for di because we don't know what that is...

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