Reposting because the first time I asked it was incorrect Please assist!! thank

Question

Reposting because the first time I asked it was incorrect

Please assist!! thank you

An object 9.5 cm tall is placed at the zero mark of a meterstick. A spherical mirror located at some point on the meterstick creates an image of the object that is upright 4.00 cm tall, and located at the 47.0-cm mark of the meter stick. Is the mirror convex or concave? convex Concave where is the mirror? At the cm mark. What kind of mirror produces an upright and diminished image? What is the mirror's focal length? Cm

Explanation / Answer

Let the mirror is at x (in cm) distance from the object

So, the object distance, u = x

and the image distance, v = -(47 - x)

Now, as the image is upright and it is shorter than the object height , it has to be a convex mirror <----- answer (a)

b)

So, using the mirror equation,

1/u + 1/v = 1/f

Now, magnifiction, m = hi/ho = 4/9.5 = -v/u

Also, v/u = (47-x)/x = 4/9.5

So, x = 33.07 cm <----------- mirror is at +33.07 cm from the object to the right

c)

1/u + 1/v = 1/f

So, 1/33.07 + 1/-(47 - 33.07) = 1/f

So, f = -24 cm <----------answer

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