(a) Where on the axis of a concave mirror would you place an object to get a half-sized image? (

step 1 Essential University Physics Volume 2 Global Edition. Chapter 31 Images and Optical Instruments.

(a) Where on the axis of a concave mirror would you place an...

Key Concepts

Real vs. Virtual Images

The nature of the image (real or virtual) in a concave mirror is determined by the object's distance from the mirror relative to the focal point. When an object is placed beyond the focal point, the mirror produces a real, inverted image that can be projected onto a screen, whereas placement within the focal point yields a virtual, upright image.

Magnification

Magnification in mirrors is defined as m = -di/do, where the negative sign indicates image inversion for real images. In problems involving the image size relative to the object, the magnification factor tells us that a half-sized image corresponds to a numerical magnification of -1/2, linking the object and image distances through the mirror equation.

Concave Mirror

A concave mirror is a spherical reflecting surface that curves inward, causing parallel rays of light to converge to a focal point. Its ability to form images depends on the object's position relative to the focal point, with distinct image characteristics when the object is placed at various distances along the principal axis.

Mirror Equation and Focal Length

The mirror equation, given by 1/f = 1/do + 1/di, relates the object distance (do), the image distance (di), and the focal length (f) of the mirror. The focal length, which is half the radius of curvature, is central to determining where an object must be placed to achieve a desired image size and location.

Transcript

00:01 Essential university physics volume 2 global edition.

00:06 Chapter 31 images and optical instruments.

00:10 Problem number 15.

00:13 Here they have asked, where on the axis of concave mirror would you place an object to get a half a sized of image? and second question is, where will the image be located? third one is, will the image be real or what? on the first hand, in the question, the axis of a concave mirror, that is when the object is placed to get half -sized rough image.

00:45 Before that, just we shall reveal this part, that is, depending on the position of the object, the magnification produced by the concave mirror may be less than or equal to or greater than one.

01:00 So, here in the conchum mirror, the magnification is the ratio of the height of the image to the height of the object.

01:11 Right.

01:12 And in the same manner, the magnification is also equal to the negative of the ratio of the distance of the image from the mirror to the distance to the object from the mirror.

01:25 And so, according to the cartesian sign convention, distances from the mirror towards object are considered as negative and the distances from the mirror to the opposite side always considered as positive.

01:45 And the distance is from the mirror above the principal axis is always considered as positive, whereas distance below the principal axis is always considered as positive, whereas distance below the principal axis, axis that is always negative.

02:02 Hence if the image is real magnification is always negative.

02:08 So we will be having the problem like this...

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