An object is 10 cm from a concave mirror that has a focal length of 5 cm . Determine image location, magnification, real or virtual, and upright or inverted for the object. a. Using the equation:
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To find the image location, we can use the mirror equation \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( f \) is the focal length, \( d_o \) is the object distance, and \( d_i \) is the image distance. Here, \( f = -5 \) cm (negative for a concave mirror) and \( d_o = -10 \) cm (also negative since the object is in front of the mirror). Plugging in the values: \[ \frac{1}{-5} = \frac{1}{-10} + \frac{1}{d_i} \] Solving for \( d_i \) gives us \( d_i = -3.33 \) cm, indicating the image is located 3.33 cm behind the mirror (a virtual image). The magnification \( m \) is given by \( m = -\frac{d_i}{d_o} \). Substituting the values provides \( m = -\frac{-3.33}{-10} = 0.33 \). A positive magnification means the image is virtual and upright. --- Diving into the journey of concave mirrors, these reflective surfaces were used in ancient times for various applications, from early telescopes to simple makeup mirrors! The fascinating aspect is how their design allows them to focus light, creating larger-than-life images – perfect for checking your hair before heading out! For maximizing your success with mirror problems, it's essential to keep track of the sign conventions: remember that distances measured in the direction of the incoming light (object side) are negative for mirrors. A common mistake is forgetting to include the negative sign for focal length and object distance, leading to confusion over whether the image is real or virtual. So double-check those signs and reflect on your calculations!
