A person wants to use a concave mirror with a focal length...

Name: Problem 17, Chapter 10: Pearson Physics 11 New South Wales Student Book
Uploaded: 2021-05-30T12:31:33-08:00
Duration: 4 min 12 s
Channel: Satpal Satpal
Description: A person wants to use a concave mirror with a focal length of 40 cm as a make-up mirror. She stands too far back and sees an image of her face that is true to size but inverted. a How far is her face from the mirror? b Where should she stand to see an upright, magnified image of herself?

A person wants to use a concave mirror with a focal length of 40 cm as a make-up mirror. She stands too far back and sees an image of her face that is true to size but inverted. a How far is her face from the mirror? b Where should she stand to see an upright, magnified image of herself?

A person wants to use a concave mirror with a focal length of 40 cm as a make-up mirror. She stands too far back and sees an image of her face that is true to size but inverted.
a How far is her face from the mirror?
b Where should she stand to see an upright, magnified image of herself?

Key Concepts

Mirror Equation

The mirror equation (1/f = 1/do + 1/di) is a fundamental relation in geometric optics that connects the focal length of a mirror, the distance of the object from the mirror (do), and the distance of the image from the mirror (di). This equation is used to predict where an image will form for any given object distance.

Magnification

Magnification is defined as the ratio of the height of the image to the height of the object, and in mirror systems it is given by m = -di/do. This value not only indicates the size change between the object and its image, but its sign also tells whether the image is upright (positive) or inverted (negative).

Real vs Virtual Images

In mirror optics, a real image is formed when light rays actually converge at a point, typically occurring when the object is placed beyond the focal length; these images are usually inverted. In contrast, a virtual image is produced when the reflected rays diverge and only appear to originate from a point behind the mirror, typically yielding an upright image when the object is placed between the mirror and its focal point.

Focal Length

The focal length of a mirror, which is the distance from the mirror to the point where parallel rays converge, is a crucial parameter that determines the image formation characteristics such as size, orientation, and whether the image is real or virtual. It sets the boundary: objects beyond the focal length produce real images, while those within yield virtual images.

Transcript

00:01 Let us first solve the first part of the problem.

00:04 As we know, magnification is equal to minus d -i divided by do, where i is image and o is the object.

00:12 So, magnification is given in this question is 1 .2, minus 1 .2.

00:17 This is minus d -i divided by do.

00:21 From here, we can write d -i is equal to 1 .2 times of d .o.

00:27 Now let's use the mirror formula.

00:29 We can write 1 divided by di plus 1 divided by do is equal to 1 divided by f or let us substitute the value so it is 1 divided by di is 1 .2 times of do plus 1 divided by do is equals to 1 divided focal length of or we can further write that distance do will be equals to 11f 11 f divided by 6 this is the relation between the object distance and the focal length so it is 11 multiplied by focal length is given as 50 cm divided by 6 and from here we get the object distance is equal to 91 .67 centimeter this is the object distance from the mirror now we need to draw the ray diagram so this is part b of this problem let's draw the ray diagram first let us draw the mirror so let this is the mirror and this is the center line and let this be the, let this is going to be, this is the focal focal point and this is the object ab, a and object a and object.

02:11 This is object.

02:12 Now let's show the ray diagram.

02:15 First we will go to hit this and it will go from the focal length of like this.

02:21 The second drive will go directly from the focal length and then rebound and then it will cut this and go like this.

02:30 This is second.

02:36 So the image formed will be at this point at this point...

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