1. The refractive index of benzene relative to water can be calculated using the formula n21 = n2/n1. Here, n2 is the refractive index of benzene (1.50) and n1 is the refractive index of water (1.33). So, n21 = 1.50/1.33 = 1.13.

2. The refractive index of air with respect to diamond is the reciprocal of the refractive index of diamond with respect to air. So, it is 1/2.5 = 0.4.

3. The wavelength of light inside the substance can be calculated using the formula λ2 = λ1/n, where λ1 is the initial wavelength and n is the refractive index. Here, λ1 = 300 nm = 3000 Ao and n = 1.5. So, λ2 = 3000/1.5 = 2000 Ao.

4. The refractive index of the second fiber relative to the first can be calculated using the formula n21 = v1/v2, where v1 and v2 are the speeds of light in the first and second fibers respectively. Here, v1 = 1.95×10^8 m/s and v2 = 2.30×10^8 m/s. So, n21 = 1.95/2.30 = 0.85 (rounded to two decimal points).

5. The time taken by the light to pass through the plastic sheet can be calculated using the formula t = d/v, where d is the thickness of the sheet and v is the speed of light in the plastic. Here, d = 5 mm = 5×10^-3 m and v = c/n, where c is the speed of light in vacuum (3×10^8 m/s) and n is the refractive index of the plastic (1.20). So, v = 3×10^8/1.20 = 2.5×10^8 m/s and t = 5×10^-3/2.5×10^8 = 2×10^-11 s.

6. The angle of reflection is equal to the angle of incidence. So, if the angle of incidence decreases by 8o, the new angle of reflection is also 30o - 8o = 22o.

7. If the image of the toy is one-third the size of the toy and is inverted, the height of the image is -1.3 cm (negative because the image is inverted). The focal length of the mirror can be calculated using the mirror formula 1/f = 1/v - 1/u, where f is the focal length, v is the image distance and u is the object distance. Here, v = -3u (because the image is one-third the size of the object and is inverted) and u = -24 cm (negative because the object is on the same side of the mirror as the light source). So, 1/f = 1/(-3u) - 1/u = -4/(3u). Solving for f gives f = -3u/4 = -3(-24)/4 = +18 cm. However, because the image is inverted, the focal length is actually negative, so the correct answer is -1.3 cm and -18 cm respectively.

Question

1. The refractive index of benzene relative to water can be calculated using the formula n21 = n2/n1. Here, n2 is the refractive index of benzene (1.50) and n1 is the refractive index of water (1.33). So, n21 = 1.50/1.33 = 1.13.

2. The refractive index of air with respect to diamond is the reciprocal of the refractive index of diamond with respect to air. So, it is 1/2.5 = 0.4.

3. The wavelength of light inside the substance can be calculated using the formula λ2 = λ1/n, where λ1 is the initial wavelength and n is the refractive index. Here, λ1 = 300 nm = 3000 Ao and n = 1.5. So, λ2 = 3000/1.5 = 2000 Ao.

4. The refractive index of the second fiber relative to the first can be calculated using the formula n21 = v1/v2, where v1 and v2 are the speeds of light in the first and second fibers respectively. Here, v1 = 1.95×10^8 m/s and v2 = 2.30×10^8 m/s. So, n21 = 1.95/2.30 = 0.85 (rounded to two decimal points).

5. The time taken by the light to pass through the plastic sheet can be calculated using the formula t = d/v, where d is the thickness of the sheet and v is the speed of light in the plastic. Here, d = 5 mm = 5×10^-3 m and v = c/n, where c is the speed of light in vacuum (3×10^8 m/s) and n is the refractive index of the plastic (1.20). So, v = 3×10^8/1.20 = 2.5×10^8 m/s and t = 5×10^-3/2.5×10^8 = 2×10^-11 s.

6. The angle of reflection is equal to the angle of incidence. So, if the angle of incidence decreases by 8o, the new angle of reflection is also 30o - 8o = 22o.

7. If the image of the toy is one-third the size of the toy and is inverted, the height of the image is -1.3 cm (negative because the image is inverted). The focal length of the mirror can be calculated using the mirror formula 1/f = 1/v - 1/u, where f is the focal length, v is the image distance and u is the object distance. Here, v = -3u (because the image is one-third the size of the object and is inverted) and u = -24 cm (negative because the object is on the same side of the mirror as the light source). So, 1/f = 1/(-3u) - 1/u = -4/(3u). Solving for f gives f = -3u/4 = -3(-24)/4 = +18 cm. However, because the image is inverted, the focal length is actually negative, so the correct answer is -1.3 cm and -18 cm respectively.

Knowee AI · Accepted Answer

1. The refractive index of benzene relative to water can be calculated using the formula n21 = n2/n1. Here, n2 is the refractive index of benzene (1.50) and n1 is the refractive index of water (1.33). So, n21 = 1.50/1.33 = 1.13.

2. The refractive index of air with respect to diamond is the reciprocal of the refractive index of diamond with respect to air. So, it is 1/2.5 = 0.4.

3. The wavelength of light inside the substance can be calculated using the formula λ2 = λ1/n, where λ1 is the initial wavelength and n is the refractive index. Here, λ1 = 300 nm = 3000 Ao and n = 1.5. So, λ2 = 3000/1.5 = 2000 Ao.

4. The refractive index of the second fiber relative to the first can be calculated using the formula n21 = v1/v2, where v1 and v2 are the speeds of light in the first and second fibers respectively. Here, v1 = 1.95×10^8 m/s and v2 = 2.30×10^8 m/s. So, n21 = 1.95/2.30 = 0.85 (rounded to two decimal points).

5. The time taken by the light to pass through the plastic sheet can be calculated using the formula t = d/v, where d is the thickness of the sheet and v is the speed of light in the plastic. Here, d = 5 mm = 5×10^-3 m and v = c/n, where c is the speed of light in vacuum (3×10^8 m/s) and n is the refractive index of the plastic (1.20). So, v = 3×10^8/1.20 = 2.5×10^8 m/s and t = 5×10^-3/2.5×10^8 = 2×10^-11 s.

6. The angle of reflection is equal to the angle of incidence. So, if the angle of incidence decreases by 8o, the new angle of reflection is also 30o - 8o = 22o.

7. If the image of the toy is one-third the size of the toy and is inverted, the height of the image is -1.3 cm (negative because the image is inverted). The focal length of the mirror can be calculated using the mirror formula 1/f = 1/v - 1/u, where f is the focal length, v is the image distance and u is the object distance. Here, v = -3u (because the image is one-third the size of the object and is inverted) and u = -24 cm (negative because the object is on the same side of the mirror as the light source). So, 1/f = 1/(-3u) - 1/u = -4/(3u). Solving for f gives f = -3u/4 = -3(-24)/4 = +18 cm. However, because the image is inverted, the focal length is actually negative, so the correct answer is -1.3 cm and -18 cm respectively.

Question

Solution

Similar Questions

Upgrade your grade with Knowee