An object is located at a distance of 100 . cm from a concave mirror of focal length 20.0 cm. A

An object is located at a distance of 100 . cm from a...

Key Concepts

Compound Mirror Systems

Compound mirror systems involve multiple mirrors arranged so that the image formed by one mirror acts as the object for the next. Analyzing these systems requires sequential application of the mirror equation and careful tracking of the sign conventions and distances between mirrors. Such systems can significantly alter both the position and the overall magnification of the final image compared to a single mirror setup.

Image Formation

Image formation in mirror systems involves determining where and how an object is reproduced as an image after reflection. This process uses the mirror equation and sign conventions to establish the nature (real or virtual) and orientation (inverted or upright) of the image. Understanding image formation is crucial when analyzing systems involving one or more mirrors.

Magnification

Magnification in mirror optics describes the ratio of the image size to the object size and is given by m = -di/do. The negative sign indicates that a positive magnification results in an inverted image. In systems with multiple mirrors, the overall magnification is obtained by multiplying the magnification factors of each mirror, cumulating the effects of successive reflections.

Mirror Equation

The mirror equation, given by 1/f = 1/do + 1/di, is fundamental in geometric optics for determining the position of an image created by a spherical mirror. This equation relates the object's distance from the mirror (do), the image's distance (di), and the mirror's focal length (f). Correctly applying this equation requires a careful attention to sign conventions to determine whether the image is real or virtual.

Concave Mirrors

Concave mirrors, which have inwardly curved reflective surfaces, are capable of converging parallel light rays to a focal point. They are commonly used in applications where real images are desired, such as in focusing devices. The properties of concave mirrors are governed by their focal lengths, and they can form inverted real images or upright virtual images depending on the object's placement relative to the focal point.

Transcript

00:01 Question belongs to the geometric optics chapter in which we have an object which is located at a distance do equals to 100 cm behind the second mirror from a concave mirror of focal length f equals to 20 centimeter.

00:15 This is the focal length of the first lens and another concave mirror of focal length f2 equals to 5 cm.

00:23 So in which we have to determine the location of the final image formed by the two mirrors and the total magnification, okay? final image location, okay, image location and the total magnification m.

00:38 We have to determine these two values.

00:41 Okay.

00:41 So for the first mirror, we can apply the line six mirror equation.

00:46 So we get one by do plus one by d .i that is equals to one by f.

00:52 So we get after substituting values, so we can write that one by d .o, which is equals to 100 cm plus 1 by d i that is equal to 1 by 20 centimeters so from here after solving di comes out to be 25 .0 centimeter okay this is the image formed by the first mirror okay so the virtual object for the mirror 2 this will be equals to distance d2 and this will be equals to minus of di i plus minus f1 okay so minus of of di this is equal to 25 cm minus f1 which is 20 centimeters so we get minus 5 point double 0 centimeter so this will be the object distance for the second mirror okay so d2 o can be written so now applying again this formula for the second mirror so we can write that 1 by d o 2 plus 1 by di 2 that is equals to 1 by f2 so substituting values so we get 1 by minus 5 plus 1 by d .i .2 that is equal to that is equals to 1 by 5.

02:06 So from here after solving we get d .i .2 that is equals to 2 .50 centimeter.

02:13 So this is the final image location of the mirror from the second mirror.

02:18 Okay.

02:21 Now we can calculate the magnification for each mirror.

02:24 So magnification for the first mirror m1, this will be equal to minus of d .i divided by d .o for the first mirror.

02:32 So minus d .i that is equals to d .i that is equals to 25 centimeter and d .o...

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