Question

A concave mirror of focal length 10cm forms an inverted image of 40cm from the mirror and 4cm high. Determine the position and size of the object by scale drawing and by calculation
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Answer 1

The equation of the constructor of the geomeric optics allows to find the results for the distance and size of the objects are:

• Distance from the mirror to the object is:  p = 13.3 cm

• The height of the object is: h = 1.33 cm

The equation of the constructor of geometric optics describes the position of objects and their images for mirrors and lenses.

       $\frac{1}{f} = \frac{1}{p} + \frac{1}{q}$  

Where f is the focal length, p and q are the distances to the object and the image, respectively.

They indicate the focal length f = 10 cm, the distance to the image q = 40 cm, that the height s h ’=  4 cm.  In the attachment we see a scheme of the system.

Let's find the distance to the object.

        $\frac{1}{p\frac{x}{y} } = \frac{1}{f} - \frac{1}{q} \\\frac{1}{p} = \frac{1}{10} - \frac{1}{40}\\\frac{1}{p} = 0.075$

       p = 13.3 cm

The magnification in the ratio of image size to object size.  The image is inverted so its height is negative.

        $m = \frac{h'}{h} = - \frac{q}{p}\\h = - \frac{p}{q} \ h'\\h = - \frac{13.3}{40}\ (-4)$

        h = 1.33 cm

In conclusion using the equation of the constructor we can find the results for the distance and size of the objects are:

• Distance from the mirror to the object is  13.3 cm

• The height of the object is 1.33 cm

   

Learn more here: brainly.com/question/14314471