I am stuck on these problems. Explanations would be helpful so I can understand

Question

I am stuck on these problems. Explanations would be helpful so I can understand it. Thanks!
1. The brightest light detected from a star has a frequency of about 7.1x10^14 Hz. What is the wavelength of this light?
2. A concave shaving mirror has a radius of curvature of 28.2 cm. For each of the following cases, find the magnification-
- an upright pencil placed 7.9 cm from the mirror
3. A convex mirror with a radius of curvature of 35.0 cm forms a 1.07 cm tall image of a pencil at a distance of 13.0 cm behind the mirror. Calculate the object distance from the pencil and its height.

Explanation / Answer

1. For electromagnetic waves, we have lambda = c/f, where lambda is the wavelength, c is the speed of light, and f is the frequency. Now we know that c = 3*10^8 m/s, and f = 7.1*10^14 Hz. So lambda = c/f = 3×10^8 / 7.1*10^14 = 4.23*10^-7 m. 2. The focal length of the mirror is half the radius of curvature, which is 28.2cm/2 = 14.1cm. Now we have 1/do + 1/di = 1/f, where do and di are object distance and image distance respectively, and f is the focal length. So 1/7.9 + 1/di = 1/14.1, di = -18.0cm. Thus, the magnification is m = -di/do = 18.0/7.9 = 2.28. 3. The focal length of the mirror is half the radius of curvature, which is 35.0cm/2 = 17.5cm. Now we have 1/do + 1/di = 1/f, where do and di are object distance and image distance respectively, and f is the focal length. So 1/do + 1/-13.0 = 1/-17.5, do = 50.6cm. And using the equation hi/ho = |di/do|, we can get ho = 1.07/13.0*50.6 = 4.16cm. Hope it's clear.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.