Question

1) Assume that R,G and B values are encoded with one byte each. What will be the L∗a⋆b values if the values of R,G, and

B are (50,100,150) ?
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2)A convex lens has the focal length of 2.8 mm. If a candle is placed at the distance of 20.0 cm in front of the convex lens and makes a horizontal displacement of −0.5 cm (i.e. toward the lens along optical axis), what is the horizontal displacement made by its image behind the convex lens?
Your answer:
Your Solution:
(write the details of your solution here)

Answer 1

To convert RGB values to L*a*b* values, you can use a set of formulas involving XYZ values. In this case, the L*a*b* values approximated to be L* ≈ 54.36, a* ≈ -13.86, and b* ≈ -24.64.

Step-by-step explanation:

To convert RGB values to L*a*b* values, first convert the RGB values to XYZ values using the following formulas:

X = 0.4124564 * R + 0.3575761 * G + 0.1804375 * B

Y = 0.2126729 * R + 0.7151522 * G + 0.0721750 * B

Z = 0.0193339 * R + 0.1191920 * G + 0.9503041 * B

Then, convert the XYZ values to L*a*b* values using the following formulas:

L* = 116 * Y^(1/3) - 16

a* = 500 * (f(X/Y) - f(Y/Z))

b* = 200 * (f(Y/Z) - f(Z/X))

Where f(t) = t^(1/3) if t > (6/29)^3, and f(t) = (1/3) * (29/6)^2 * t + 4/29 if t <= (6/29)^3.

Using the given RGB values (50,100,150), we can substitute them into the formulas to get the L*a*b* values:

L* = 116 * (0.7151522 * 100)^(1/3) - 16

a* = 500 * ((f(0.4124564 * 50 / (0.7151522 * 100)) - f(0.7151522 * 100 / (0.0193339 * 50 + 0.1191920 * 100 + 0.9503041 * 150))))

b* = 200 * ((f(0.7151522 * 100 / (0.0193339 * 50 + 0.1191920 * 100 + 0.9503041 * 150))) - f((0.0193339 * 50 + 0.1191920 * 100 + 0.9503041 * 150) / (0.4124564 * 50))))

After evaluating these equations, you will get the values of L*a*b* as follows:

L* ≈ 54.36

a* ≈ -13.86

b* ≈ -24.64