A metal spoon acts approximately as a spherical mirror. The...

A metal spoon acts approximately as a spherical mirror. The spoon in Figure $\mathrm{P} 24.56$ produces an upright image of an object. a. Is the "front" of the spoon (the side that would hold soup) facing toward the object or away from it? b. If a person holds the spoon at arm's length and uses it as a mirror to view herself, what is the approximate magnification of the image?

A metal spoon acts approximately as a spherical mirror. The spoon in Figure $\mathrm{P} 24.56$ produces an upright image of an object.
a. Is the "front" of the spoon (the side that would hold soup) facing toward the object or away from it?
b. If a person holds the spoon at arm's length and uses it as a mirror to view herself, what is the approximate magnification of the image?

Key Concepts

Spherical Mirrors

Spherical mirrors use a portion of a sphere’s surface as the reflecting area. Their behavior is dictated by the mirror equation, which relates object distance, image distance, and focal length. A key aspect is that the curvature (and thus, the focal length) determines whether the mirror is concave or convex, which in turn affects image orientation and size.

Concave vs Convex Surfaces

A concave (inward?curved) mirror can produce either a real, inverted image or a virtual, upright image depending on the object’s position relative to its focal point. When an object is placed closer to a concave mirror than its focal length, the image is virtual, upright, and magnified. In contrast, a convex (outward?curved) mirror always produces virtual, upright, and diminished images. Recognizing which side of a curved surface is being used is crucial for predicting image properties.

Virtual Images

Virtual images are formed when the reflected rays only appear to diverge from a common point behind the mirror. They cannot be cast on a screen. In both convex mirrors and concave mirrors (when the object is inside the focal length), the resulting virtual images are upright compared to the object.

Mirror Equation and Magnification

The mirror equation, 1/u + 1/v = 1/f, together with the magnification formula, m = -v/u, provide quantitative tools for determining the position, size, and nature (real or virtual) of an image. For instance, using these relationships one can explain how holding a mirror (or spoon) at different distances causes changes in magnification—whether the image appears enlarged or reduced relative to the object.

Transcript

0:00 Hello everyone.

00:01 Let us do the following question.

00:03 In this question we will say that a metal spoon acts approximately as a spherical mirror.

00:09 The spoon produces an upright image of the object.

00:12 The spoon produces an upright image of the objector.

00:15 Is the front of the spoon facing towards the objector away from it? if a person holds the spoon at arm's length and uses it as a mirror to view herself, what is the approximate magnification? we have to calculate the what is the value for a approximate magnification.

00:32 Here we will say that the magnification is the value for the magnification is written as the magnification is written as value for magnification is equals to minus s i divided by s not.

00:52 We can make responsible estimates from the for the spoon radius of curvature and object distance and then compute the image distance from the mirror equation.

01:03 From this we will get value 1 by s node plus 1 by s s is equal to 1 by f.

01:11 This will be equal to 2 by r.

01:15 This will be equal to 2 by r.

01:17 So we will say that as given in the question, the spoon produces an upright image.

01:25 The spoon produces an upright image.

01:26 The spoon produces an upright image the spoon produces an upright image and so so it must be concave so it must be concave so it must be concave thus the front of the spoon must face away thus the front of the spoon does the front of the spoon must the fade away.

02:05 Must fade away.

02:08 Next, we will say that spoon has a radius of curvature.

02:13 Spoon has a radius of curvature of 2 cm and the person holds it 50 cm away...

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