The nature of the image is magnified , virtual , and upright.
<h3>Further explanation</h3>
We will solve this problem using following formula:
![\large{ \boxed {\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}}}](https://tex.z-dn.net/?f=%5Clarge%7B%20%5Cboxed%20%7B%5Cfrac%7B1%7D%7Bs_o%7D%20%2B%20%5Cfrac%7B1%7D%7Bs_i%7D%20%3D%20%5Cfrac%7B1%7D%7Bf%7D%7D%7D)
where:
<em>so = distance of object from mirror</em>
<em>si = distance of image from mirror</em>
<em>f = focal length of mirror</em>
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<u>Given:</u>
Magnification = M = 1
Initial Image Distance = si = 30 cm
Difference of Object's Distance = Δso = 20 cm
<u>Unknown:</u>
Final Image Distance = si' = ?
<u>Solution:</u>
<h3>
Initial Condition:</h3>
![M = \frac{s_i}{s_o}](https://tex.z-dn.net/?f=M%20%3D%20%5Cfrac%7Bs_i%7D%7Bs_o%7D)
![1 = \frac{s_i}{s_o}](https://tex.z-dn.net/?f=1%20%3D%20%5Cfrac%7Bs_i%7D%7Bs_o%7D)
![s_i = s_o](https://tex.z-dn.net/?f=s_i%20%3D%20s_o)
![s_o = 30 cm](https://tex.z-dn.net/?f=s_o%20%3D%2030%20cm)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
![\frac{1}{s_o} + \frac{1}{s_i} = \frac{1}{f}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bs_o%7D%20%2B%20%5Cfrac%7B1%7D%7Bs_i%7D%20%3D%20%5Cfrac%7B1%7D%7Bf%7D)
![\frac{1}{s_o} + \frac{1}{s_o} = \frac{1}{f}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bs_o%7D%20%2B%20%5Cfrac%7B1%7D%7Bs_o%7D%20%3D%20%5Cfrac%7B1%7D%7Bf%7D)
![\frac{2}{s_o} = \frac{1}{f}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bs_o%7D%20%3D%20%5Cfrac%7B1%7D%7Bf%7D)
![f = \frac{1}{2} s_o](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20s_o)
![f = \frac{1}{2} \times 30](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%2030)
![f = 15 \texttt{ cm}](https://tex.z-dn.net/?f=f%20%3D%2015%20%5Ctexttt%7B%20cm%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Final Condition:</h3>
![s_o' = s_o - \Delta s](https://tex.z-dn.net/?f=s_o%27%20%3D%20s_o%20-%20%5CDelta%20s)
![s_o' = 30 - 20](https://tex.z-dn.net/?f=s_o%27%20%3D%2030%20-%2020)
![s_o' = 10 \texttt{ cm}](https://tex.z-dn.net/?f=s_o%27%20%3D%2010%20%5Ctexttt%7B%20cm%7D)
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
![\frac{1}{s_o'} + \frac{1}{s_i'} = \frac{1}{f}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bs_o%27%7D%20%2B%20%5Cfrac%7B1%7D%7Bs_i%27%7D%20%3D%20%5Cfrac%7B1%7D%7Bf%7D)
![\frac{1}{10} + \frac{1}{s_i'} = \frac{1}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%20%2B%20%5Cfrac%7B1%7D%7Bs_i%27%7D%20%3D%20%5Cfrac%7B1%7D%7B15%7D)
![\frac{1}{s_i'} = \frac{1}{15} - \frac{1}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bs_i%27%7D%20%3D%20%5Cfrac%7B1%7D%7B15%7D%20-%20%5Cfrac%7B1%7D%7B10%7D)
![\frac{1}{s_i'} = \frac{2}{30} - \frac{3}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bs_i%27%7D%20%3D%20%5Cfrac%7B2%7D%7B30%7D%20-%20%5Cfrac%7B3%7D%7B30%7D)
![\frac{1}{s_i'} = -\frac{1}{30}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bs_i%27%7D%20%3D%20-%5Cfrac%7B1%7D%7B30%7D)
![s_i' = 30 \texttt{ cm}](https://tex.z-dn.net/?f=s_i%27%20%3D%2030%20%5Ctexttt%7B%20cm%7D)
Because si' < 0 , the nature of the image will be magnified , virtual , and upright.
![\texttt{ }](https://tex.z-dn.net/?f=%5Ctexttt%7B%20%7D)
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Physics
Chapter: Light
Keywords: Light , Mirror , Magnification , Ray , Diagram , Image , Real , Virtual